A sample of 37 observations is selected from a normal population. The sample mean is 29, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level.
H
0
: μ ≤ 26
H
1
: μ > 26
a.
Is this a one- or two-tailed test?
H
0
,
when z > evidence to conclude that the population mean is greater than 26.
e.
What is the
p
-value?
(Round your answer to 4 decimal places.)
At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $82 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $3.26. Over the first 44 days she was employed at the restaurant, the mean daily amount of her tips was $84.61. At the 0.02 significance level, can Ms. Brigden conclude that her daily tips average more than $82?
a.
State the null hypothesis and the alternate hypothesis.
H
0
. The mean number of calls is than 39 per week.
United Nations report shows the mean family income for Mexican migrants to the United States is $28,540 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 28 Mexican family units reveals a mean to be $34,120 with a sample standard deviation of $10,050. Does this information disagree with the United Nations report? Apply the 0.01 significance level.
a.
State the null hypothesis and the alternate hypothesis.
H
0
:
μ
=
. This data
the report.
The following information is available.
H
0
: μ ≥ 220
H
1
: μ < 220
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level.
a.
Is this a one- or two-tailed test?
H
0
when
z
<
H
0
. There is evidence to conclude that the population mean is greater than 10
Given the following hypotheses:
H
0
: μ = 400
H
1
: μ ≠ 400
A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:
a.
State the decision rule.
(Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)
Reject
H
0
when the test statistic is the interval ([removed], [removed]).
b.
Compute the value of the test statistic.
(Round your answer to 3 decimal places.)
Value of the test statistic
[removed]
c.
What is your decision regarding the null hypothesis?
[removed]
Reject
[removed]
Do not reject
p
-value
[removed]
p
-value
[removed]
p
-value
[removed]
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[The following information applies to the questions displayed belo.docxdanielfoster65629
[The following information applies to the questions displayed below.]
A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.01 significance level.
H0: μ ≤ 10
H1: μ > 10
1.
Value:
10.00 points
Required information
a.
Is this a one- or two-tailed test?
One-tailed test
Two-tailed test
References
EBook & Resources
Multiple Choice Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
2.
Value:
10.00 points
Required information
b.
What is the decision rule?
Reject H0 when z ≤ 2.326
Reject H0 when z > 2.326
References
EBook & Resources
Multiple Choice Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
3.
Value:
10.00 points
Required information
c.
What is the value of the test statistic?
Value of the test statistic
References
EBook & Resources
Worksheet Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
4.
Value:
10.00 points
Required information
d.
What is your decision regarding H0?
Fail to reject H0
Reject H0
References
EBook & Resources
Multiple Choice Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
5.
Value:
10.00 points
Required information
e.
What is the p-value?
p-value
References
Given the following hypotheses:
H0 : μ = 400
H1 : μ ≠ 400
A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:
a.
State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)
Reject H0 when the test statistic is the interval (,).
b.
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
c.
What is your decision regarding the null hypothesis?
Do not reject
Reject
The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?
a.
What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Rej.
1) A sample of 47 observations is selected from a normal popul.docxSONU61709
1) A sample of 47 observations is selected from a normal population. The sample mean is 31, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.
H0 : μ ≤ 30
H1 : μ > 30
a.
Is this a one- or two-tailed test?
"One-tailed"-the alternate hypothesis is greater than direction.
"Two-tailed"-the alternate hypothesis is different from direction.
b.
What is the decision rule? (Round your answer to 3 decimal places.)
H0, when z >
c.
What is the value of the test statistic? (Round your answer to 2 decimal places.)
Value of the test statistic
d.
What is your decision regarding H0?
Reject
Do not reject
There is evidence to conclude that the population mean is greater than 30.
e.
What is the p-value? (Round your answer to 4 decimal places.)
p-value
2) At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $86 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $3.81. Over the first 48 days she was employed at the restaurant, the mean daily amount of her tips was $87.07. At the 0.02 significance level, can Ms. Brigden conclude that her daily tips average more than $86?
a.
State the null hypothesis and the alternate hypothesis.
H0: μ = 86 ; H1: μ ≠ 86
H0: μ ≥ 86 ; H1: μ < 86
H0: μ ≤ 86 ; H1: μ > 86
H0: μ >86 ; H1: μ = 86
b.
State the decision rule.
Reject H0 if z > 2.05
Reject H1 if z < 2.05
Reject H0 if z < 2.05
Reject H1 if z > 2.05
c.
Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
d.
What is your decision regarding H0?
Reject H0
Do not reject H0
e.
What is the p-value? (Round your answer to 4 decimal places.)
p-value
3) The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 37 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 41 sales representatives reveals that the mean number of calls made last week was 40. The standard deviation of the sample is 5.6 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 37?
H0 : μ ≤ 37
H1 : μ > 37
1.
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
2.
What is your decision regarding H0?
H0. The mean number of calls is than 37 per week.
4) A United Nations report shows the mean family income for Mexican migrants to the United States is $27,540 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 19 Mexican family units reveals a mean to be $28,956 with a sample standard deviation of $10,250. Does this information disagree with the United Nations report? Apply the 0.01 significance level.
a.
St ...
The document discusses hypothesis testing methodology and steps. It defines key terms like the null hypothesis, alternative hypothesis, type I and type II errors, and level of significance. It then covers the z-test for the mean when the population standard deviation is known, including the steps to conduct the test and examples comparing means and proportions from independent samples.
Introduction to hypothesis testing ppt @ bec domsBabasab Patil
This document introduces hypothesis testing, including:
- Formulating null and alternative hypotheses for tests involving population means and proportions
- Using test statistics, critical values, and p-values to test hypotheses
- Defining Type I and Type II errors and their probabilities
- Examples of hypothesis tests for means (using z-tests and t-tests) and proportions (using z-tests) are provided to illustrate the concepts.
This document provides an introduction to hypothesis testing, including:
1. Defining hypotheses as claims about population parameters and the distinction between the null and alternative hypotheses.
2. Explaining the hypothesis testing process, including specifying the significance level, determining the rejection region, calculating test statistics, and making a decision.
3. Providing examples of one-sample z-tests and t-tests for the mean when the population standard deviation is known and unknown.
4. Discussing type I and type II errors and how significance levels influence the probability of each.
JKN 10 Inference 2 Populations.Consider the following set of d.docxchristiandean12115
JKN 10 Inference 2 Populations.
Consider the following set of data.
Pairs
1
2
3
4
5
Sample A
9
4
3
5
3
Sample B
3
8
2
7
1
(a) Find the paired differences, d = A - B, for this set of data.
(d1)
(d2)
(d3)
(d4)
(d5)
(b) Find the mean d of the paired differences. (Give your answer correct to one decimal place.)
(c) Find the standard deviation sd of the paired differences. (Give your answer correct to two decimal places.)
Salt-free diets are often prescribed to people with high blood pressure. The following data values were obtained from an experiment designed to estimate the reduction in diastolic blood pressure as a result of consuming a salt-free diet for 2 weeks. Eight subjects had their blood pressure measured and then ate a salt free diet for two weeks and had their blood pressure measured again. Assume diastolic readings to be normally distributed.
Before
99
105
93
102
100
108
107
97
After
92
102
91
94
96
98
100
93
(a) The proper TI-83 program to use to compute the confidence interval for the mean reduction in blood pressure is:
(b) Find the 98% confidence interval for the mean reduction. (Give your answers correct to two decimal places.)
Lower Limit
Upper Limit
(c) Which of the following statements is true about the confidence interval? (More than one may apply)
We are 98% confident that the true mean of the individual differences in blood pressure is in the intervalIf we took 100 samples and constructed 100 confidence intervals for the mean of the individual differences, approximately 98 of them would contain the true mean of the individual differencesWe are 98 % confident that the mean of the after data minus the mean of the before data is in the intervalWe are 98 % confident that the mean of the before data minus the mean of the after data is in the interval
An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were litter-mates. The rations were assigned at random to the two animals within each pair. The gains (in pounds) after 45 days are shown in the following table. Assuming weight gain is normal, find the 99% confidence interval estimate for the mean of the differences μd, where d = ration A - ration B. (Give your answers correct to two decimal places.)
Litter
1
2
3
4
5
6
7
8
Ration A
56
40
60
59
43
40
50
46
Ration B
54
30
50
56
37
36
42
40
Lower Limit
Upper Limit
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims.
(a) There is an increase in the mean difference between post-test and pretest scores.(d=post-test scores - pretest scores)
Ho: μd
0
Ha: μd
0
(b) Following a special training session, it is believed that the mean of the difference in performance scores will not be zero.
Ho: μd
0
Ha: μd
0
(c) On average, there is no difference between the readings from two inspectors on .
Please put answers below the boxes1) A politician claims that .docxLeilaniPoolsy
Please put answers below the boxes
1)
A politician claims that he is supported by a clear majority of voters. In a recent survey, 35 out of 51 randomly selected voters indicated that they would vote for the politician. Use a 5% significance level for the test. Use Table 1.
a.
Select the null and the alternative hypotheses.
H0: p = 0.50; HA: p ≠ 0.50
H0: p ≤ 0.50; HA: p > 0.50
H0: p ≥ 0.50; HA: p < 0.50
b.
Calculate the sample proportion. (Round your answer to 3 decimal places.)
Sample proportion
c.
Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)
Test statistic
d.
Calculate the p-value of the test statistic. (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and final answer to 4 decimal places.)
p-value
e.
What is the conclusion?
Do not reject H0; the politician is not supported by a clear majority
Do not reject H0; the politician is supported by a clear majority
Reject H0; the politician is not supported by a clear majority
Reject H0; the politician is supported by a clear majority
2)
Consider the following contingency table.
B
Bc
A
22
24
Ac
28
26
a.
Convert the contingency table into a joint probability table. (Round your intermediate calculations and final answers to 4 decimal places.)
B
Bc
Total
A
Ac
Total
b.
What is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)
Probability
c.
What is the probability that A and B occur? (Round your intermediate calculations and final answer to 4 decimal places.)
Probability
d.
Given that B has occurred, what is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)
Probability
e.
Given that Ac has occurred, what is the probability that B occurs? (Round your intermediate calculations and final answer to 4 decimal places.)
Probability
f.
Are A and B mutually exclusive events?
Yes because P(A | B) ≠ P(A).
Yes because P(A ∩ B) ≠ 0.
No because P(A | B) ≠ P(A).
No because P(A ∩ B) ≠ 0.
g.
Are A and B independent events?
Yes because P(A | B) ≠ P(A).
Yes because P(A ∩ B) ≠ 0.
No because P(A | B) ≠ P(A).
No because P(A ∩ B) ≠ 0.
3)
A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 72, 55, 49, 35, 39, 23, and 77. It can be assumed that weekday customer visits follow a normal distribution. Use Table 2.
a.
Construct a 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places and "t" value to 3 decimal places, and final answers to 2 decimal places.)
Confidence interval
to
b.
Construct a 99% confidence interval for the average number of customers who visit the .
[The following information applies to the questions displayed belo.docxdanielfoster65629
[The following information applies to the questions displayed below.]
A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.01 significance level.
H0: μ ≤ 10
H1: μ > 10
1.
Value:
10.00 points
Required information
a.
Is this a one- or two-tailed test?
One-tailed test
Two-tailed test
References
EBook & Resources
Multiple Choice Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
2.
Value:
10.00 points
Required information
b.
What is the decision rule?
Reject H0 when z ≤ 2.326
Reject H0 when z > 2.326
References
EBook & Resources
Multiple Choice Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
3.
Value:
10.00 points
Required information
c.
What is the value of the test statistic?
Value of the test statistic
References
EBook & Resources
Worksheet Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
4.
Value:
10.00 points
Required information
d.
What is your decision regarding H0?
Fail to reject H0
Reject H0
References
EBook & Resources
Multiple Choice Difficulty: 2 Intermediate Learning Objective: 10-05 Conduct a test of a hypothesis about a population mean.
eBook: Conduct a test of a hypothesis about a population mean.
Check my work
5.
Value:
10.00 points
Required information
e.
What is the p-value?
p-value
References
Given the following hypotheses:
H0 : μ = 400
H1 : μ ≠ 400
A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:
a.
State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)
Reject H0 when the test statistic is the interval (,).
b.
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
c.
What is your decision regarding the null hypothesis?
Do not reject
Reject
The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?
a.
What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Rej.
1) A sample of 47 observations is selected from a normal popul.docxSONU61709
1) A sample of 47 observations is selected from a normal population. The sample mean is 31, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.
H0 : μ ≤ 30
H1 : μ > 30
a.
Is this a one- or two-tailed test?
"One-tailed"-the alternate hypothesis is greater than direction.
"Two-tailed"-the alternate hypothesis is different from direction.
b.
What is the decision rule? (Round your answer to 3 decimal places.)
H0, when z >
c.
What is the value of the test statistic? (Round your answer to 2 decimal places.)
Value of the test statistic
d.
What is your decision regarding H0?
Reject
Do not reject
There is evidence to conclude that the population mean is greater than 30.
e.
What is the p-value? (Round your answer to 4 decimal places.)
p-value
2) At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $86 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $3.81. Over the first 48 days she was employed at the restaurant, the mean daily amount of her tips was $87.07. At the 0.02 significance level, can Ms. Brigden conclude that her daily tips average more than $86?
a.
State the null hypothesis and the alternate hypothesis.
H0: μ = 86 ; H1: μ ≠ 86
H0: μ ≥ 86 ; H1: μ < 86
H0: μ ≤ 86 ; H1: μ > 86
H0: μ >86 ; H1: μ = 86
b.
State the decision rule.
Reject H0 if z > 2.05
Reject H1 if z < 2.05
Reject H0 if z < 2.05
Reject H1 if z > 2.05
c.
Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
d.
What is your decision regarding H0?
Reject H0
Do not reject H0
e.
What is the p-value? (Round your answer to 4 decimal places.)
p-value
3) The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 37 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 41 sales representatives reveals that the mean number of calls made last week was 40. The standard deviation of the sample is 5.6 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 37?
H0 : μ ≤ 37
H1 : μ > 37
1.
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
2.
What is your decision regarding H0?
H0. The mean number of calls is than 37 per week.
4) A United Nations report shows the mean family income for Mexican migrants to the United States is $27,540 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 19 Mexican family units reveals a mean to be $28,956 with a sample standard deviation of $10,250. Does this information disagree with the United Nations report? Apply the 0.01 significance level.
a.
St ...
The document discusses hypothesis testing methodology and steps. It defines key terms like the null hypothesis, alternative hypothesis, type I and type II errors, and level of significance. It then covers the z-test for the mean when the population standard deviation is known, including the steps to conduct the test and examples comparing means and proportions from independent samples.
Introduction to hypothesis testing ppt @ bec domsBabasab Patil
This document introduces hypothesis testing, including:
- Formulating null and alternative hypotheses for tests involving population means and proportions
- Using test statistics, critical values, and p-values to test hypotheses
- Defining Type I and Type II errors and their probabilities
- Examples of hypothesis tests for means (using z-tests and t-tests) and proportions (using z-tests) are provided to illustrate the concepts.
This document provides an introduction to hypothesis testing, including:
1. Defining hypotheses as claims about population parameters and the distinction between the null and alternative hypotheses.
2. Explaining the hypothesis testing process, including specifying the significance level, determining the rejection region, calculating test statistics, and making a decision.
3. Providing examples of one-sample z-tests and t-tests for the mean when the population standard deviation is known and unknown.
4. Discussing type I and type II errors and how significance levels influence the probability of each.
JKN 10 Inference 2 Populations.Consider the following set of d.docxchristiandean12115
JKN 10 Inference 2 Populations.
Consider the following set of data.
Pairs
1
2
3
4
5
Sample A
9
4
3
5
3
Sample B
3
8
2
7
1
(a) Find the paired differences, d = A - B, for this set of data.
(d1)
(d2)
(d3)
(d4)
(d5)
(b) Find the mean d of the paired differences. (Give your answer correct to one decimal place.)
(c) Find the standard deviation sd of the paired differences. (Give your answer correct to two decimal places.)
Salt-free diets are often prescribed to people with high blood pressure. The following data values were obtained from an experiment designed to estimate the reduction in diastolic blood pressure as a result of consuming a salt-free diet for 2 weeks. Eight subjects had their blood pressure measured and then ate a salt free diet for two weeks and had their blood pressure measured again. Assume diastolic readings to be normally distributed.
Before
99
105
93
102
100
108
107
97
After
92
102
91
94
96
98
100
93
(a) The proper TI-83 program to use to compute the confidence interval for the mean reduction in blood pressure is:
(b) Find the 98% confidence interval for the mean reduction. (Give your answers correct to two decimal places.)
Lower Limit
Upper Limit
(c) Which of the following statements is true about the confidence interval? (More than one may apply)
We are 98% confident that the true mean of the individual differences in blood pressure is in the intervalIf we took 100 samples and constructed 100 confidence intervals for the mean of the individual differences, approximately 98 of them would contain the true mean of the individual differencesWe are 98 % confident that the mean of the after data minus the mean of the before data is in the intervalWe are 98 % confident that the mean of the before data minus the mean of the after data is in the interval
An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were litter-mates. The rations were assigned at random to the two animals within each pair. The gains (in pounds) after 45 days are shown in the following table. Assuming weight gain is normal, find the 99% confidence interval estimate for the mean of the differences μd, where d = ration A - ration B. (Give your answers correct to two decimal places.)
Litter
1
2
3
4
5
6
7
8
Ration A
56
40
60
59
43
40
50
46
Ration B
54
30
50
56
37
36
42
40
Lower Limit
Upper Limit
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims.
(a) There is an increase in the mean difference between post-test and pretest scores.(d=post-test scores - pretest scores)
Ho: μd
0
Ha: μd
0
(b) Following a special training session, it is believed that the mean of the difference in performance scores will not be zero.
Ho: μd
0
Ha: μd
0
(c) On average, there is no difference between the readings from two inspectors on .
Please put answers below the boxes1) A politician claims that .docxLeilaniPoolsy
Please put answers below the boxes
1)
A politician claims that he is supported by a clear majority of voters. In a recent survey, 35 out of 51 randomly selected voters indicated that they would vote for the politician. Use a 5% significance level for the test. Use Table 1.
a.
Select the null and the alternative hypotheses.
H0: p = 0.50; HA: p ≠ 0.50
H0: p ≤ 0.50; HA: p > 0.50
H0: p ≥ 0.50; HA: p < 0.50
b.
Calculate the sample proportion. (Round your answer to 3 decimal places.)
Sample proportion
c.
Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)
Test statistic
d.
Calculate the p-value of the test statistic. (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and final answer to 4 decimal places.)
p-value
e.
What is the conclusion?
Do not reject H0; the politician is not supported by a clear majority
Do not reject H0; the politician is supported by a clear majority
Reject H0; the politician is not supported by a clear majority
Reject H0; the politician is supported by a clear majority
2)
Consider the following contingency table.
B
Bc
A
22
24
Ac
28
26
a.
Convert the contingency table into a joint probability table. (Round your intermediate calculations and final answers to 4 decimal places.)
B
Bc
Total
A
Ac
Total
b.
What is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)
Probability
c.
What is the probability that A and B occur? (Round your intermediate calculations and final answer to 4 decimal places.)
Probability
d.
Given that B has occurred, what is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)
Probability
e.
Given that Ac has occurred, what is the probability that B occurs? (Round your intermediate calculations and final answer to 4 decimal places.)
Probability
f.
Are A and B mutually exclusive events?
Yes because P(A | B) ≠ P(A).
Yes because P(A ∩ B) ≠ 0.
No because P(A | B) ≠ P(A).
No because P(A ∩ B) ≠ 0.
g.
Are A and B independent events?
Yes because P(A | B) ≠ P(A).
Yes because P(A ∩ B) ≠ 0.
No because P(A | B) ≠ P(A).
No because P(A ∩ B) ≠ 0.
3)
A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 72, 55, 49, 35, 39, 23, and 77. It can be assumed that weekday customer visits follow a normal distribution. Use Table 2.
a.
Construct a 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places and "t" value to 3 decimal places, and final answers to 2 decimal places.)
Confidence interval
to
b.
Construct a 99% confidence interval for the average number of customers who visit the .
1. The document discusses hypothesis testing methodology and various hypothesis testing processes. It covers topics like the null and alternative hypotheses, type 1 and type 2 errors, and significance levels.
2. Several examples of hypothesis testing are provided, including testing means using z-tests and t-tests, and testing proportions using z-tests. The steps of hypothesis testing are outlined.
3. Factors that affect the probability of type 2 errors are discussed, such as the significance level, population standard deviation, and sample size.
The document discusses confidence interval estimation and hypothesis testing. It introduces key concepts such as point estimates, interval estimates, confidence intervals, null and alternative hypotheses, significance levels, test statistics, decision rules, and p-values. Examples are provided to illustrate how to construct confidence intervals for means and proportions, determine sample sizes, and conduct hypothesis tests for single means using z-tests and t-tests.
1) The document discusses statistical inference and hypothesis testing. It covers topics like point and interval estimation, confidence intervals, hypothesis testing steps and terminology, tests for population means and proportions, and chi-square tests for independence.
2) An example calculates a 95% confidence interval for the mean hours students work per week based on sample data.
3) The final section discusses contingency tables and chi-square tests, providing an example to test if hand dominance and gender are associated using a contingency table. It shows calculating expected frequencies and the chi-square test statistic to evaluate the null hypothesis of independence.
This document provides an overview of hypothesis testing concepts including:
- A hypothesis is a claim about a population parameter that can be tested statistically. The null hypothesis states the claim to be tested, while the alternative hypothesis is what the researcher is trying to prove.
- The level of significance and critical values determine the rejection region where the null hypothesis would be rejected. Type I and Type II errors refer to incorrectly rejecting or failing to reject the null hypothesis.
- The key steps of hypothesis testing are stated as: 1) specify null and alternative hypotheses, 2) choose significance level and sample size, 3) determine test statistic, 4) find critical values, 5) collect data and compute test statistic, 6) make a decision
This document provides solutions to practice problems for hypothesis testing. It tests claims about population parameters such as drug failure rates and textbook prices against sample data. For each problem it states the null and alternative hypotheses, calculates the test statistic, finds the critical value, and makes a decision to reject or fail to reject the null hypothesis. It defines type I and type II errors and explains how lower variation in test scores does not necessarily indicate students are performing better.
Int 150 The Moral Instinct”1. Most cultures agree that abus.docxmariuse18nolet
Int 150
“The Moral Instinct”
1. Most cultures agree that abusing innocent people is wrong. True or false
2. Young children have a sense of morality. True or false (example)?
3. Emotional reasoning trumps rationalizing. True or false (explain)
4. According to the article, psychopathy or moral misbehavior (like rape) is more environmental than genetic. True or false (example)
5. Explain the point about the British schoolteacher in Sudan.
6. Name three things anthropologists believe all people share, in addition to thinking it’s bad to harm others and good to help them.
a.
b.
c.
7. What is reciprocal altruism?
8. How does the psychologist Tetlock explain the outrage of American college students at the thought that adoption agencies should place children with couples willing to pay the most?
9. Discuss: A love for children and sense of justice is just an expression of our innate sense of preserving our genes for future generations (Darwin)
10. What does the author warn about the arguments regarding climate change?
Hypothesis Testing
(Statistical Significance)
1
Hypothesis Testing
Goal: Make statement(s) regarding unknown population parameter values based on sample data
Elements of a hypothesis test:
Null hypothesis - Statement regarding the value(s) of unknown parameter(s). Typically will imply no association between explanatory and response variables in our applications (will always contain an equality)
Alternative hypothesis - Statement contradictory to the null hypothesis (will always contain an inequality)
The level of significant (Alpha) is the maximum probability of committing a type I error. P(type I error)= alpha
Definitions
Rejection (alpha, α) Region:
Represents area under the curve that is used to reject the null hypothesis
Level of Confidence, 1 - alpha (a):
Also known as fail to reject (FTR) region
Represents area under the curve that is used to fail to reject the null hypothesis
FTR
H0
α/2
α/2
3
1 vs. 2 Sided Tests
Two-sided test
No a priori reason 1 group should have stronger effect
Used for most tests
Example
H0: μ1 = μ2
HA: μ1 ≠ μ2
One-sided test
Specific interest in only one direction
Not scientifically relevant/interesting if reverse situation true
Example
H0: μ1 ≤ μ2
HA: μ1 > μ2
4
Example: It is believed that the mean age of smokers in San Bernardino is 47. Researchers from LLU believe that the average age is different than 47.
Hypothesis
H0:μ = 47
HA: μ ≠ 47
μ = 47
α /2 = 0.025
Fail to Reject (FTR)
α /2 = 0.025
5
Three Approaches to Reject or Fail to Reject A Null Hypothesis:
1a. Confidence interval
Calculate the confidence interval
Decision Rule:
a. If the confidence interval (CI) includes the null, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) does not include the null, then the decision must be to reject the H0.
6
1b. Confidence interval to compare groups
Calculate the confidence interval for each gro.
This document provides an overview of common statistical hypothesis tests, including:
1. One-tail and two-tail t-tests of hypotheses for the mean to compare a sample mean to a hypothesized population mean or compare two independent sample means.
2. Z-tests of hypotheses for a proportion to test a claim about a population proportion or compare two independent proportions.
3. Pooled variance t-tests to compare two independent sample means when population variances are unknown but assumed equal.
Worked examples are provided to demonstrate how to set up the null and alternative hypotheses, calculate test statistics, determine critical values, and make decisions to reject or fail to reject the null hypothesis.
This document discusses four hypothesis tests and confidence intervals:
1) A z-test finds the average annual income was less than $50,000 based on a p-value less than 0.05.
2) A z-test for proportion finds insufficient evidence the proportion of urban customers exceeds 40% with a p-value greater than 0.05.
3) A z-test finds insufficient evidence the average years lived in a home is less than 13 based on a p-value greater than 0.05.
4) A z-test finds the average credit balance for suburban customers is more than $4,300 based on a p-value less than 0.05.
Week 5 HomeworkHomework #1Ms. Lisa Monnin is the budget dire.docxmelbruce90096
Week 5 Homework
Homework #1
Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.
Sales ($)
129
137
142
162
137
145
Audit ($)
128
98
128
140
148
110
132
At the 0.1 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff?
(a)
State the decision rule. (Round your answer to 3 decimal places.)
Reject H0 if t >
(b)
Compute the pooled estimate of the population variance. (Round your answer to 2 decimal places.)
Pooled variance
(c)
Compute the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
(d)
State your decision about the null hypothesis.
H0 : μs ≤ μa
(e)
Estimate the p-value. (Round your answers to 3 decimal places.)
p-value
Homework #2
Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. Assume the population standard deviations are not the same. The following is the amount ($000) earned per month by a sample of Claiborne models:
$5.4
$4.3
$3.7
$6.7
$4.9
$5.9
$3.1
$5.2
$4.7
$3.5
5.8
4
3.1
5.6
6.9
The following is the amount ($000) earned by a sample of Klein models.
$2.5
$2.6
$3.5
$3.4
$2.8
$3.1
$4
$2.5
$2
$2.9
2.7
2.3
(1)
Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)
Degrees of freedom
(2)
State the decision rule for 0.01 significance level: H0: μLC ≤ μCK; H1: μLC > μCK. (Round your answer to 3 decimal places.)
Reject H0 if t>
(3)
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
(4)
Is it reasonable to conclude that Claiborne models earn more? Use the 0.01 significance level.
H0. It is to conclude that Claiborne models earn more.
Homework #3
A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below.
Statistic
Men
Women
Sample mean
23.82
21.38
Population standard deviation
5.91
4.87
Sample size
34
36
At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?
(a)
Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
(b)
What is your decision regarding on null hypothesis?
The decision is the null hypothesis that the means are the same.
(c)
What is the p-value? (Round your answer to 4 decimal places.)
p-value
rev: 04_04_2012, 04_25_2014_QC_48145
Homework #4
Suppose the manufacturer of Advil, a common headache remedy, recently developed a new formulation of the drug that is claimed to be more effective. To evaluate the new drug, a s.
Hypothesis Testing techniques in social research.pptSolomonkiplimo
1) This document discusses hypothesis testing and comparing populations. It covers developing null and alternative hypotheses, types of errors, significance levels, and approaches using p-values and critical values.
2) Key steps in hypothesis testing include specifying the null and alternative hypotheses, choosing a significance level, calculating a test statistic, and determining whether to reject the null based on the p-value or critical value.
3) Comparing two populations involves testing whether their means are equal or different. The standard deviations play a role in determining if sample means are close enough to indicate the true population means are probably the same or different.
The quiz has two portions Multiple Choice (8 problems, 32 p.docxhelen23456789
The quiz has two portions:
Multiple Choice
(8 problems, 32 points).
Show work/explanation as appropriate
.
Short Answer
(3 problems, 38 points)
Show work
.
MULTIPLE CHOICE
. Choose the one alternative that best completes the statement or answers the question.
(
4 points
) If the P-value of a hypothesis test comparing two means was 0.25, what can you conclude? (Select all that apply):
A. You can accept the null hypothesis
B. There was a significant difference between the means
C. You failed to reject the null hypothesis
D. There did not appear to be significant difference between the means
(
4 points
) Imagine a researcher wanted to test the effect of the new drug on reducing blood pressure. In this study, there were 50 participants. The researcher measured the participants’ blood pressure before and after the drug intake. If we want to compare the mean blood pressure from the two time periods with a two-tailed t test, how many degrees of freedom are there?
A. 49
B. 50
C. 99
D. 100
(
4 points
) When sample size increases, ____
A. Power increases a great degree at first, reaches its peak, and then slowly decreases
B. Power decreases a great degree at first, reaches its lowest point, and then slowly increases
C. Power increases a great degree at first, and then increases slowly
D. Power decreases a great degree at first, and then decreases slowly
(
4 points
) α=0.05 for a two-tailed test. Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.
A. ±1.768
B. ±1.764
C. ±1.96
D. ±2.575
(
4 points
) In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.
A. 0.0024
B. 0.0524
C. 0.0228
D. 0.0048
(
4 points
) For a simple random sample, the size is n=17, σ is not known, and the original population is normally distributed. Determine whether the give conditions justify testing a claim about a population mean µ.
A. Yes
B. No
(
4 points
) A medical researcher claims that 20% of children suffer from a certain disorder. Indentify the type I error for the test.
A. Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 20% when the percentage is actually 20%.
B. Reject the claim that the percentage of children who suffer from the disorder is equal to 20% when that percentage is actually 20%.
C. Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 20% when that percentage is actually different from 20%.
D.Reject the claim that the percentage of children who suffer from the disorder is different from 20% when that percentage really is different f.
The document discusses Chi Square distribution and analysis of frequency using Fisher's exact test and McNemar's test. It provides the assumptions, data arrangement, hypotheses, test statistic, decision rules, and example application of both tests for categorical paired and unpaired data. Fisher's exact test is used for 2x2 contingency tables when sample sizes are small, while McNemar's test analyzes paired nominal data to evaluate hypotheses about proportions between pairs.
This document discusses the process of testing hypotheses. It begins by defining hypothesis testing as a way to make decisions about population characteristics based on sample data, which involves some risk of error. The key steps are outlined as:
1) Formulating the null and alternative hypotheses, with the null hypothesis stating no difference or relationship.
2) Computing a test statistic based on the sample data and selecting a significance level, usually 5%.
3) Comparing the test statistic to critical values to either reject or fail to reject the null hypothesis.
Examples are provided to demonstrate hypothesis testing for a single mean, comparing two means, and testing a claim about population characteristics using sample data and statistics.
Statistics practice for finalBe sure to review the following.docxdessiechisomjj4
Statistics practice for final
Be sure to review the following and have this information handy when taking Final GHA:
· Calculating z alpha/2 and t alpha/2 on Tables II and IV
· Find sample size for estimating population mean. Formula 8.3 p. 321 OCR.
· Stating H0 and H1 claims about variation and about the mean. Chapter 9 OCR.
· Type I and Type II errors p. 345 OCR.
· Confidence Interval for difference between two population means. Chapter 10 OCR p. 428
· Pooled sample standard deviation. Chapter 10 OCR p. 397
· What do Chi-Square tests measure? How are their degrees of freedom calculated? Chapter 12 OCR
· Find F test statistic using One-Way ANOVA.xls Be sure to enable editing and change values to match your problem. One-Way ANOVA.xls
· Find equation of regression line used to predict. To do on Excel, go to a blank worksheet, enter x values in one column and their matching y values in another column. Click Insert – Select Scatterplot. Right click any one of the points (diamonds) on the graph. Left click “Add a Trendline.” Check “Display Equation on Chart” box. Regression equation will appear on chart. Try it here with No. 20 below.
Practice Problems
Chapter 8 Final Review
1) In which of the following situations is it reasonable to use the z-interval
procedure to obtain a confidence interval for the population mean?
Assume that the population standard deviation is known.
A. n = 10, the data contain no outliers, the variable under consideration is
not normally distributed.
B. n = 10, the variable under consideration is normally distributed.
C. n = 18, the data contain no outliers, the variable under consideration is
far from being normally distributed.
D. n = 18, the data contain outliers, the variable under consideration is
normally distributed.
Find the necessary sample size.
2) The weekly earnings of students in one age group are normally
distributed with a standard deviation of 10 dollars. A researcher wishes to
estimate the mean weekly earnings of students in this age group. Find the
sample size needed to assure with 95 percent confidence that the sample
mean will not differ from the population mean by more than 2 dollars.
Find the specified t-value.
3) For a t-curve with df = 6, find the two t-values that divide the area under
the curve into a middle 0.99 area and two outside areas of 0.005.
Provide an appropriate response.
4) Under what conditions would you choose to use the t-interval procedure
instead of the z-interval procedure in order to obtain a confidence
interval for a population mean? What conditions must be satisfied in
order to use the t-interval procedure?
CHAPTER 8 Answers
1) B
2) 97
3) -3.707, 3.707
4) When the population standard deviation is unknown, the t-interval procedure is used instead of the
z-interval procedure. The t-interval procedure works provided that the population is normally
distributed or the.
Testing hypothesis (methods of testing the statement of organizations)syedahadisa929
My ppt is about the testing hypothesis which is used in statistics to check whether the statement of company, organization, or institution is true or false
This document discusses hypothesis testing and the t-test. It covers:
1) The basics of hypothesis testing including null and alternative hypotheses, types of hypotheses, and types of errors.
2) The t-test, which is used for small samples from a normally distributed population. It relies on the t-distribution and the degree of freedom.
3) Applications of the t-test including testing the significance of a single mean, difference between two means, and paired t-tests.
4) When sample sizes are large, the normal distribution can be used instead in Z-tests for similar applications.
C2 st lecture 10 basic statistics and the z test handoutfatima d
This document provides an overview of basic statistics concepts including averages, measures of dispersion, hypothesis testing, and the z-test. It defines the mode, median, mean, interquartile range, standard deviation, and absolute deviation. It explains how to perform a z-test including writing the null and alternative hypotheses, looking up the critical value, calculating the test statistic, and making a decision. Two examples of z-tests are provided to demonstrate the process.
This document summarizes the Wilcoxon signed-rank test, a nonparametric test used to test hypotheses about the median or location of a population when the assumptions of the t-test are not met. It provides an example applying the test to data on cardiac output measurements from 15 patients. The test calculates the differences between each observation and the hypothesized median, ranks the absolute values of the differences, and sums the ranks with positive and negative signs. The smaller of the two sums is the test statistic, which is compared to a critical value to determine if the null hypothesis that the population median equals the hypothesized value can be rejected.
Discuss three (3) ways that large organizations are increasingly eng.docxrhetttrevannion
Discuss three (3) ways that large organizations are increasingly engaging in social entrepreneurship and the importance of stakeholder relationships in this effort.
Describe the concept of ‘Third Sector’ innovation and reflect on the motive of non-profit entrepreneurial organizations to service these social needs. Next explain how the concept of uneven global distribution of innovation influences this sector. Provide examples to support your rationale.
I am adding a web link for you to review, here are a few web links on Social Entrepreneurship
1. From Forbes.com here is a list of several young social entrepreneurs.
http://www.forbes.com/special-report/2012/30-under-30/30-under-30_social.html
2.
From Stanford University:
Social Entrepreneurship: the case for Definition.
http://ssir.org/articles/entry/social_entrepreneurship_the_case_for_definition
.
Discuss this week’s objectives with your team sharing related rese.docxrhetttrevannion
Discuss
this week’s objectives with your team sharing related research, connections and applications made by individual team members.
Prepare
a 350- to 1,050- word Reflection from the learning that took place in your team forum with:
·
An introduction
·
A body that uses the objectives as headings (2.1, 2.2, 2.3, & 2.4 spelled out). After commenting on or defining the objectives (no names) include a couple of individual team member’s specific connections and/or applications by name.
·
A conclusion that highlights a few specifics from the body of the Reflection.
·
A reference page that lists the e-text plus at least two other sources.
.
More Related Content
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1. The document discusses hypothesis testing methodology and various hypothesis testing processes. It covers topics like the null and alternative hypotheses, type 1 and type 2 errors, and significance levels.
2. Several examples of hypothesis testing are provided, including testing means using z-tests and t-tests, and testing proportions using z-tests. The steps of hypothesis testing are outlined.
3. Factors that affect the probability of type 2 errors are discussed, such as the significance level, population standard deviation, and sample size.
The document discusses confidence interval estimation and hypothesis testing. It introduces key concepts such as point estimates, interval estimates, confidence intervals, null and alternative hypotheses, significance levels, test statistics, decision rules, and p-values. Examples are provided to illustrate how to construct confidence intervals for means and proportions, determine sample sizes, and conduct hypothesis tests for single means using z-tests and t-tests.
1) The document discusses statistical inference and hypothesis testing. It covers topics like point and interval estimation, confidence intervals, hypothesis testing steps and terminology, tests for population means and proportions, and chi-square tests for independence.
2) An example calculates a 95% confidence interval for the mean hours students work per week based on sample data.
3) The final section discusses contingency tables and chi-square tests, providing an example to test if hand dominance and gender are associated using a contingency table. It shows calculating expected frequencies and the chi-square test statistic to evaluate the null hypothesis of independence.
This document provides an overview of hypothesis testing concepts including:
- A hypothesis is a claim about a population parameter that can be tested statistically. The null hypothesis states the claim to be tested, while the alternative hypothesis is what the researcher is trying to prove.
- The level of significance and critical values determine the rejection region where the null hypothesis would be rejected. Type I and Type II errors refer to incorrectly rejecting or failing to reject the null hypothesis.
- The key steps of hypothesis testing are stated as: 1) specify null and alternative hypotheses, 2) choose significance level and sample size, 3) determine test statistic, 4) find critical values, 5) collect data and compute test statistic, 6) make a decision
This document provides solutions to practice problems for hypothesis testing. It tests claims about population parameters such as drug failure rates and textbook prices against sample data. For each problem it states the null and alternative hypotheses, calculates the test statistic, finds the critical value, and makes a decision to reject or fail to reject the null hypothesis. It defines type I and type II errors and explains how lower variation in test scores does not necessarily indicate students are performing better.
Int 150 The Moral Instinct”1. Most cultures agree that abus.docxmariuse18nolet
Int 150
“The Moral Instinct”
1. Most cultures agree that abusing innocent people is wrong. True or false
2. Young children have a sense of morality. True or false (example)?
3. Emotional reasoning trumps rationalizing. True or false (explain)
4. According to the article, psychopathy or moral misbehavior (like rape) is more environmental than genetic. True or false (example)
5. Explain the point about the British schoolteacher in Sudan.
6. Name three things anthropologists believe all people share, in addition to thinking it’s bad to harm others and good to help them.
a.
b.
c.
7. What is reciprocal altruism?
8. How does the psychologist Tetlock explain the outrage of American college students at the thought that adoption agencies should place children with couples willing to pay the most?
9. Discuss: A love for children and sense of justice is just an expression of our innate sense of preserving our genes for future generations (Darwin)
10. What does the author warn about the arguments regarding climate change?
Hypothesis Testing
(Statistical Significance)
1
Hypothesis Testing
Goal: Make statement(s) regarding unknown population parameter values based on sample data
Elements of a hypothesis test:
Null hypothesis - Statement regarding the value(s) of unknown parameter(s). Typically will imply no association between explanatory and response variables in our applications (will always contain an equality)
Alternative hypothesis - Statement contradictory to the null hypothesis (will always contain an inequality)
The level of significant (Alpha) is the maximum probability of committing a type I error. P(type I error)= alpha
Definitions
Rejection (alpha, α) Region:
Represents area under the curve that is used to reject the null hypothesis
Level of Confidence, 1 - alpha (a):
Also known as fail to reject (FTR) region
Represents area under the curve that is used to fail to reject the null hypothesis
FTR
H0
α/2
α/2
3
1 vs. 2 Sided Tests
Two-sided test
No a priori reason 1 group should have stronger effect
Used for most tests
Example
H0: μ1 = μ2
HA: μ1 ≠ μ2
One-sided test
Specific interest in only one direction
Not scientifically relevant/interesting if reverse situation true
Example
H0: μ1 ≤ μ2
HA: μ1 > μ2
4
Example: It is believed that the mean age of smokers in San Bernardino is 47. Researchers from LLU believe that the average age is different than 47.
Hypothesis
H0:μ = 47
HA: μ ≠ 47
μ = 47
α /2 = 0.025
Fail to Reject (FTR)
α /2 = 0.025
5
Three Approaches to Reject or Fail to Reject A Null Hypothesis:
1a. Confidence interval
Calculate the confidence interval
Decision Rule:
a. If the confidence interval (CI) includes the null, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) does not include the null, then the decision must be to reject the H0.
6
1b. Confidence interval to compare groups
Calculate the confidence interval for each gro.
This document provides an overview of common statistical hypothesis tests, including:
1. One-tail and two-tail t-tests of hypotheses for the mean to compare a sample mean to a hypothesized population mean or compare two independent sample means.
2. Z-tests of hypotheses for a proportion to test a claim about a population proportion or compare two independent proportions.
3. Pooled variance t-tests to compare two independent sample means when population variances are unknown but assumed equal.
Worked examples are provided to demonstrate how to set up the null and alternative hypotheses, calculate test statistics, determine critical values, and make decisions to reject or fail to reject the null hypothesis.
This document discusses four hypothesis tests and confidence intervals:
1) A z-test finds the average annual income was less than $50,000 based on a p-value less than 0.05.
2) A z-test for proportion finds insufficient evidence the proportion of urban customers exceeds 40% with a p-value greater than 0.05.
3) A z-test finds insufficient evidence the average years lived in a home is less than 13 based on a p-value greater than 0.05.
4) A z-test finds the average credit balance for suburban customers is more than $4,300 based on a p-value less than 0.05.
Week 5 HomeworkHomework #1Ms. Lisa Monnin is the budget dire.docxmelbruce90096
Week 5 Homework
Homework #1
Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.
Sales ($)
129
137
142
162
137
145
Audit ($)
128
98
128
140
148
110
132
At the 0.1 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff?
(a)
State the decision rule. (Round your answer to 3 decimal places.)
Reject H0 if t >
(b)
Compute the pooled estimate of the population variance. (Round your answer to 2 decimal places.)
Pooled variance
(c)
Compute the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
(d)
State your decision about the null hypothesis.
H0 : μs ≤ μa
(e)
Estimate the p-value. (Round your answers to 3 decimal places.)
p-value
Homework #2
Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. Assume the population standard deviations are not the same. The following is the amount ($000) earned per month by a sample of Claiborne models:
$5.4
$4.3
$3.7
$6.7
$4.9
$5.9
$3.1
$5.2
$4.7
$3.5
5.8
4
3.1
5.6
6.9
The following is the amount ($000) earned by a sample of Klein models.
$2.5
$2.6
$3.5
$3.4
$2.8
$3.1
$4
$2.5
$2
$2.9
2.7
2.3
(1)
Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.)
Degrees of freedom
(2)
State the decision rule for 0.01 significance level: H0: μLC ≤ μCK; H1: μLC > μCK. (Round your answer to 3 decimal places.)
Reject H0 if t>
(3)
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
(4)
Is it reasonable to conclude that Claiborne models earn more? Use the 0.01 significance level.
H0. It is to conclude that Claiborne models earn more.
Homework #3
A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below.
Statistic
Men
Women
Sample mean
23.82
21.38
Population standard deviation
5.91
4.87
Sample size
34
36
At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?
(a)
Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
(b)
What is your decision regarding on null hypothesis?
The decision is the null hypothesis that the means are the same.
(c)
What is the p-value? (Round your answer to 4 decimal places.)
p-value
rev: 04_04_2012, 04_25_2014_QC_48145
Homework #4
Suppose the manufacturer of Advil, a common headache remedy, recently developed a new formulation of the drug that is claimed to be more effective. To evaluate the new drug, a s.
Hypothesis Testing techniques in social research.pptSolomonkiplimo
1) This document discusses hypothesis testing and comparing populations. It covers developing null and alternative hypotheses, types of errors, significance levels, and approaches using p-values and critical values.
2) Key steps in hypothesis testing include specifying the null and alternative hypotheses, choosing a significance level, calculating a test statistic, and determining whether to reject the null based on the p-value or critical value.
3) Comparing two populations involves testing whether their means are equal or different. The standard deviations play a role in determining if sample means are close enough to indicate the true population means are probably the same or different.
The quiz has two portions Multiple Choice (8 problems, 32 p.docxhelen23456789
The quiz has two portions:
Multiple Choice
(8 problems, 32 points).
Show work/explanation as appropriate
.
Short Answer
(3 problems, 38 points)
Show work
.
MULTIPLE CHOICE
. Choose the one alternative that best completes the statement or answers the question.
(
4 points
) If the P-value of a hypothesis test comparing two means was 0.25, what can you conclude? (Select all that apply):
A. You can accept the null hypothesis
B. There was a significant difference between the means
C. You failed to reject the null hypothesis
D. There did not appear to be significant difference between the means
(
4 points
) Imagine a researcher wanted to test the effect of the new drug on reducing blood pressure. In this study, there were 50 participants. The researcher measured the participants’ blood pressure before and after the drug intake. If we want to compare the mean blood pressure from the two time periods with a two-tailed t test, how many degrees of freedom are there?
A. 49
B. 50
C. 99
D. 100
(
4 points
) When sample size increases, ____
A. Power increases a great degree at first, reaches its peak, and then slowly decreases
B. Power decreases a great degree at first, reaches its lowest point, and then slowly increases
C. Power increases a great degree at first, and then increases slowly
D. Power decreases a great degree at first, and then decreases slowly
(
4 points
) α=0.05 for a two-tailed test. Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.
A. ±1.768
B. ±1.764
C. ±1.96
D. ±2.575
(
4 points
) In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.
A. 0.0024
B. 0.0524
C. 0.0228
D. 0.0048
(
4 points
) For a simple random sample, the size is n=17, σ is not known, and the original population is normally distributed. Determine whether the give conditions justify testing a claim about a population mean µ.
A. Yes
B. No
(
4 points
) A medical researcher claims that 20% of children suffer from a certain disorder. Indentify the type I error for the test.
A. Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 20% when the percentage is actually 20%.
B. Reject the claim that the percentage of children who suffer from the disorder is equal to 20% when that percentage is actually 20%.
C. Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 20% when that percentage is actually different from 20%.
D.Reject the claim that the percentage of children who suffer from the disorder is different from 20% when that percentage really is different f.
The document discusses Chi Square distribution and analysis of frequency using Fisher's exact test and McNemar's test. It provides the assumptions, data arrangement, hypotheses, test statistic, decision rules, and example application of both tests for categorical paired and unpaired data. Fisher's exact test is used for 2x2 contingency tables when sample sizes are small, while McNemar's test analyzes paired nominal data to evaluate hypotheses about proportions between pairs.
This document discusses the process of testing hypotheses. It begins by defining hypothesis testing as a way to make decisions about population characteristics based on sample data, which involves some risk of error. The key steps are outlined as:
1) Formulating the null and alternative hypotheses, with the null hypothesis stating no difference or relationship.
2) Computing a test statistic based on the sample data and selecting a significance level, usually 5%.
3) Comparing the test statistic to critical values to either reject or fail to reject the null hypothesis.
Examples are provided to demonstrate hypothesis testing for a single mean, comparing two means, and testing a claim about population characteristics using sample data and statistics.
Statistics practice for finalBe sure to review the following.docxdessiechisomjj4
Statistics practice for final
Be sure to review the following and have this information handy when taking Final GHA:
· Calculating z alpha/2 and t alpha/2 on Tables II and IV
· Find sample size for estimating population mean. Formula 8.3 p. 321 OCR.
· Stating H0 and H1 claims about variation and about the mean. Chapter 9 OCR.
· Type I and Type II errors p. 345 OCR.
· Confidence Interval for difference between two population means. Chapter 10 OCR p. 428
· Pooled sample standard deviation. Chapter 10 OCR p. 397
· What do Chi-Square tests measure? How are their degrees of freedom calculated? Chapter 12 OCR
· Find F test statistic using One-Way ANOVA.xls Be sure to enable editing and change values to match your problem. One-Way ANOVA.xls
· Find equation of regression line used to predict. To do on Excel, go to a blank worksheet, enter x values in one column and their matching y values in another column. Click Insert – Select Scatterplot. Right click any one of the points (diamonds) on the graph. Left click “Add a Trendline.” Check “Display Equation on Chart” box. Regression equation will appear on chart. Try it here with No. 20 below.
Practice Problems
Chapter 8 Final Review
1) In which of the following situations is it reasonable to use the z-interval
procedure to obtain a confidence interval for the population mean?
Assume that the population standard deviation is known.
A. n = 10, the data contain no outliers, the variable under consideration is
not normally distributed.
B. n = 10, the variable under consideration is normally distributed.
C. n = 18, the data contain no outliers, the variable under consideration is
far from being normally distributed.
D. n = 18, the data contain outliers, the variable under consideration is
normally distributed.
Find the necessary sample size.
2) The weekly earnings of students in one age group are normally
distributed with a standard deviation of 10 dollars. A researcher wishes to
estimate the mean weekly earnings of students in this age group. Find the
sample size needed to assure with 95 percent confidence that the sample
mean will not differ from the population mean by more than 2 dollars.
Find the specified t-value.
3) For a t-curve with df = 6, find the two t-values that divide the area under
the curve into a middle 0.99 area and two outside areas of 0.005.
Provide an appropriate response.
4) Under what conditions would you choose to use the t-interval procedure
instead of the z-interval procedure in order to obtain a confidence
interval for a population mean? What conditions must be satisfied in
order to use the t-interval procedure?
CHAPTER 8 Answers
1) B
2) 97
3) -3.707, 3.707
4) When the population standard deviation is unknown, the t-interval procedure is used instead of the
z-interval procedure. The t-interval procedure works provided that the population is normally
distributed or the.
Testing hypothesis (methods of testing the statement of organizations)syedahadisa929
My ppt is about the testing hypothesis which is used in statistics to check whether the statement of company, organization, or institution is true or false
This document discusses hypothesis testing and the t-test. It covers:
1) The basics of hypothesis testing including null and alternative hypotheses, types of hypotheses, and types of errors.
2) The t-test, which is used for small samples from a normally distributed population. It relies on the t-distribution and the degree of freedom.
3) Applications of the t-test including testing the significance of a single mean, difference between two means, and paired t-tests.
4) When sample sizes are large, the normal distribution can be used instead in Z-tests for similar applications.
C2 st lecture 10 basic statistics and the z test handoutfatima d
This document provides an overview of basic statistics concepts including averages, measures of dispersion, hypothesis testing, and the z-test. It defines the mode, median, mean, interquartile range, standard deviation, and absolute deviation. It explains how to perform a z-test including writing the null and alternative hypotheses, looking up the critical value, calculating the test statistic, and making a decision. Two examples of z-tests are provided to demonstrate the process.
This document summarizes the Wilcoxon signed-rank test, a nonparametric test used to test hypotheses about the median or location of a population when the assumptions of the t-test are not met. It provides an example applying the test to data on cardiac output measurements from 15 patients. The test calculates the differences between each observation and the hypothesized median, ranks the absolute values of the differences, and sums the ranks with positive and negative signs. The smaller of the two sums is the test statistic, which is compared to a critical value to determine if the null hypothesis that the population median equals the hypothesized value can be rejected.
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A sample of 37 observations is selected from a normal population. Th.docx
1. A sample of 37 observations is selected from a normal
population. The sample mean is 29, and the population standard
deviation is 5. Conduct the following test of hypothesis using
the 0.05 significance level.
H
0
: μ ≤ 26
H
1
: μ > 26
a.
Is this a one- or two-tailed test?
H
0
,
when z > evidence to conclude that the population mean is
greater than 26.
e.
What is the
p
-value?
(Round your answer to 4 decimal places.)
At the time she was hired as a server at the Grumney Family
Restaurant, Beth Brigden was told, “You can average $82 a day
in tips.” Assume the population of daily tips is normally
distributed with a standard deviation of $3.26. Over the first 44
2. days she was employed at the restaurant, the mean daily amount
of her tips was $84.61. At the 0.02 significance level, can Ms.
Brigden conclude that her daily tips average more than $82?
a.
State the null hypothesis and the alternate hypothesis.
H
0
. The mean number of calls is than 39 per week.
United Nations report shows the mean family income for
Mexican migrants to the United States is $28,540 per year. A
FLOC (Farm Labor Organizing Committee) evaluation of 28
Mexican family units reveals a mean to be $34,120 with a
sample standard deviation of $10,050. Does this information
disagree with the United Nations report? Apply the 0.01
significance level.
a.
State the null hypothesis and the alternate hypothesis.
H
0
:
μ
=
. This data
the report.
The following information is available.
H
3. 0
: μ ≥ 220
H
1
: μ < 220
A sample of 64 observations is selected from a normal
population. The sample mean is 215, and the population
standard deviation is 15. Conduct the following test of
hypothesis using the .025 significance level.
a.
Is this a one- or two-tailed test?
H
0
when
z
<
H
0
. There is evidence to conclude that the population mean is
greater than 10
Given the following hypotheses:
H
0
: μ = 400
H
4. 1
: μ ≠ 400
A random sample of 12 observations is selected from a normal
population. The sample mean was 407 and the sample standard
deviation 6. Using the .01 significance level:
a.
State the decision rule.
(Negative amount should be indicated by a minus sign. Round
your answers to 3 decimal places.)
Reject
H
0
when the test statistic is the interval ([removed], [removed]).
b.
Compute the value of the test statistic.
(Round your answer to 3 decimal places.)
Value of the test statistic
[removed]
c.
What is your decision regarding the null hypothesis?
[removed]
Reject
[removed]
Do not reject
p
-value
6. (
1
)
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