Unit 3 Problem Set NAME: Elements of Statistics--FHSU Virtual College--Spring 2017 REMEMBER, these are assessed preparatory problems related to the content of Unit 3. The Unit 3 Exam will consist of similar types of

1. Elements of Statistics
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Unit 3 Problem Set NAME: Elements of Statistics--FHSU Virtual
College--Spring 2017
REMEMBER, these are assessed preparatory problems related to the
content of Unit 3. The Unit 3 Exam will consist of similar types of
problems, but not exactly the same. Thus, make sure you are thinking
about the concepts and procedures you studied in this unit versus
simply “copying” the process of an example problem. Also, take time
to examine the complete objective list in the Unit 3 Review
document.
Listed out to the left of the spreadsheet are text chapter separators if
you find yourself needing some direction to a related resource. All
answers should be calculated, as needed, within this Excel sheet, and
final concluding answers given directly below or to the right of the
problem. Please make your answers are easily found--for example use
a different color or type of font. No numerical answer resulting
from a calculation will be accepted unless the process is performed in
Excel and formulas/calculations used are evident when the
cell is selected.
Also, note that the templates for hypothesis testing provided in the
Excel Guides for this unit are also given in the next worksheet in this
document--see folder tabs at the bottom of the sheet. You may use
these templates by copying from the second worksheet, pasting the

2. copy to the right of the associated problem, then changing values as
needed.
Problems related to text's Chapter 7:
1. Assume you need to build a confidence interval for a population
mean within some given situation. Naturally, you must determine
whether
you should use either the t-distribution or the z-distribution or
possibly even neither based upon the information known/collected in
the
situation. Thus, based upon the information provided for each
situation below, determine which (t-, z- or neither) distribution is
appropriate.
Then if you can use either a t- or z- distribution, give the associated
critical value (critical t- or z- score) from that distribution to reach the
given
confidence level.
a. 99% confidence
n=75
Appropriate distribution:
Associated critical value: σ known population data believed to be very
skewed d. 95% confidence
n=8
Appropriate distribution:
Associated critical value: σ known population data believed to be very
skewed c. 90% confidence
n=73

3. Appropriate distribution:
Associated critical value: σ unknown population data believed to be
skewed e. 99% confidence
n=10
Appropriate distribution:
Associated critical value: σ unknown population data believed to be
normally distributed 2. The data below shows the birth weights (in
kilograms) of thirty randomly chosen male babies born in Hays
Medical in past year. It is also known that the
population standard deviation of birth weights for all male babies
born is 0.0731 kg (based on data from the New York State
Department of Health). 3.73
3.96
2.55 4.37
2.21
3.44 3.73
2.67
3.07 4.33
4.09
4.23 3.3
3.02
2.92 3.39
2.76
3.55 3.68

4. 3.67
3.92 4.68
3.76
3.41 3.72
3.45
4.14 a. How do you know that you will need to construct the
confidence interval using a z-distribution approach as opposed to a
tdistribution? We want to construct the mean value confidence
interval for all Hays male babies' birth weights with a 99% confidence
level.
b. Determine the best point estimate (average) for the mean birth
weight. c. Determine the critical z-value(s) associated with the 99%
confidence level. d. Determine the margin of error. e. Determine the
confidence interval. f. In a sentence, interpret the contextual meaning
of your result to part e above...that is relate the values to this situation
regarding
the mean birth weights of all Hays male babies born. 3.02
2.54
3.15 3. Determine the two chi-squared (χ2) critical values for the
following confidence levels and sample sizes.
a. 98% and n=25 b. 90% and n=60 4. We are also interested in
estimating the population standard deviation for all male babies birth
weights (in kilograms). We will assume that
birth weights are at least approximately normally distributed. Below
are the birth weights of 30 randomly chosen male babies from Hays
Medical. 3.73
3.96

5. 2.55 4.37
2.21
3.44 3.73
2.67
3.07 4.33
4.09
4.23 3.3
3.02
2.92 3.39
2.76
3.55 3.68
3.67
3.92 4.68
3.76
3.41 3.72
3.45
4.14 Out to the right, construct a 99% confidence interval estimate of
sigma (σ), the population standard deviation. Problems related to
text's Chapter 8:
5. (Multiple Choice) A hypothesis test is used to test a claim. On a
right-tailed hypothesis test with a 1.39 critical value, the collected
sample's

6. test statistic is calculated to be 1.41. Which of the following is the
correct decision statement for the test? A. Fail to reject the null
hypothesis
B. Reject the null hypothesis
C. Claim the alternative hypothesis is true
D. Claim the null hypothesis is false 6. (Multiple Choice) A
hypothesis test is used to test a claim. A P-value of 0.001 is calculated
on the hypothesis test with a significance level set at 0.01. Which of
the following is the correct decision statement for the test?
A. Claim the null hypothesis is true
B. Claim the alternative hypothesis is false
C. Reject the null hypothesis
D. Fail to reject the null hypothesis 7. (Multiple Answers) Which of
the following is not a requirement for using the t-distribution for a
hypothesis test concerning μ.
A. Sample is a simple random sample
B. The population is normally distributed
C. The population standard deviation is known
D. The sample size is greater than 30
8. A report by the NCAA states that 57.5% of football injuries occur
during practices. A head trainer claims that this is too high for his
conference,
so he randomly selects 36 injuries and finds that 18 occurred during
practices.
a. Is the above information sufficient for you to be completely agree
with the head trainer, that the percentage of football injuries

7. occur during practices is less than 57.5%? Why or why not? b. In
establishing a statistical hypothesis testing of this situation, give the
required null and alternative hypotheses for such a test, if it
is desired that the percentage of football injuries occur during
practices is less than 57.5%.
H0:
H1: c. Based on your answer in part b, should you use a right-tailed, a
left-tailed, or a two-tailed test? Briefly explain how one determines
which of the three possibilities is to be used. d. Describe the possible
Type I error for this situation--make sure to state the error in terms of
the percent of football injuries occur
during practices. 3.02
2.54
3.15 e. Describe the possible Type II error for this situation--make
sure to state the error in terms of the percent of football injuries occur
during practices. f. Determine the appropriate critical value(s) for this
situation given a 0.05 significance level. g. Determine/calculate the
value of the sample test statistic. h. Detemine the P-value. i. Based
upon your work above, is there statistically sufficient evidence in this
sample to support that less than 57.5% injuries occur
at practice for this conference? Briefly explain your reasoning. 0
9. The mean score on a certain achievement test at the turn of the
century was 73. However, national standards have been implmented
which
may lead to a change in the mean score. A random sample of 48
scores on this exam taken this year yeilded the following data set. At
a

8. 10% significance level, test the claim that the mean of all current test
scores is the same as in 2000.
85
77
74
88
89
66
0
70
73
76
86
74
73
82
72
0
82
82
80
76

9. 87
76
77
67
72
49
73
75
82
73
81
30
58
75
72
89
76
18
72
74
60

10. 88
20
99
50
35
78
66
a. Give the null and alternative hypotheses for this test in symbolic
form.
H0:
H1:
b. Determine the value of the test statistic. c. Determine the
appropriate critical value(s). d Detemine the P-value. e. Is there
sufficient evidence to warrant rejection of the claim that the mean
achivement score is now is 73, the same as in 2000?
Explain your reasoning. Problem related to text's Chapter 9:
10. Listed below are pretest and posttest scores from a study. Using a
5% significance level, is there statistically sufficient evidence to
support
the claim that the posttest scores were the higher than the pretest
scores? Perform an appropriate hypothesis test showing necessary
statistical evidence to support your final given conclusion.
PreTest
24

11. 11
14
25
17
28
22 PostTest
25
18
16
29
16
29
25 Problems related to text's Chapter 10:
11. Multiple Choice:
For each of the following data sets, choose the most appropriate
response from the choices below the table.
Data Set #1
Data Set #2
x
y
x
y

12. 0.3
3790
-1
-4
0.4
3354
-2
-10
0.5
2986
2
5
0.6
2613
3
4
0.7
2277
-3
-19
0.8

13. 1765
6
-10
0.9
1343
7
-20
1
1151
-1
-4
1.1
510
0
1
A. A strong positive linear relation exists
A. A strong positive linear relation exists
B. A strong negative linear relation exists
B. A strong negative linear relation exists
C. A curvilinear relation exists
C. A curvilinear relation exists

14. D. No linear relation exists
D. No linear relation exists 12. Give a real life example of two
variables that are likely to be negatively correlated. Specifically
explain why you believe they are negatively
correlated. 13. To answer the following, use the given data set for
lengths (in inches) and corresponding weights (in pounds) of
randomly selected black
bears captured in the backcountry of Colorado
lengths (inches) weights (pounds)
40
65
64
256
65
216
49
94
47
86
59
189
61
202

15. 49
102
a.
Construct a scatterplot for this data set in the region to the right
(length as the independent variable, and weight as the dependent.)
b. Based on the scatterplot, does it look like a linear regression model
is appropriate for this data? Why or why not? c. Add the line-of-best
fit (trend line/linear regression line) to your scatterplot. Give the
equation of the trend line below. Then give
the slope value of the line and explain its meaning to this context. d.
Determine the value of the correlation coefficient. Explain what the
value tells you about the data pairs? e. Does the value of the
correlation coefficient tell you there is or is not statistically significant
evidence that correlation exists
between the length and weight of black bears? Explain your position.
(HINT: application of table A-6 is needed!) f. Based on the above,
what is the best predicted weight of a bear with a length of 45 inches?
Templates for Hypothesis Testing As stated on the practice exam
document, below you will find templates you may use in completing
this
the one you need, copy it to where you are working, and then input
the proper values for the problem yo
related to the labels in red. Single Sample Proportion Test:
Two-tailed Proportion
significance level (alpha)
p=
x=
n= 0.01

16. 0.82
56
73 q=
0.18
p-hat = 0.7671232877
critical values are: -2.575829304 and
test statistic = -1.175933319
P-value = 0.2396215232 2.575829 Single Sample Mean Test (or
difference in matched paired two samp
Two-tailed Mean (sigma known)
significance level (alpha)
x-bar =
mu, μ =
sigma, σ =
n= 0.05
24.85
24
2
25 critical values are: -1.959963985 and
test statistic =
2.125

17. P-value = 0.0335866129 1.959964 Two-tailed Mean (sigma
unknown)
significance level (alpha)
0.05
x-bar =
110
mu, μ =
118
s=
12
n=
20
critical values are: -2.093024054 and
test statistic = -2.98142397
P-value = 0.0076706134 2.093024 Single Sample Variance/Standard
Deviation Test
Two-tailed Standard Deviation
significance level (alpha)
n= 0.05
25 s=
σ= 0.029
0.023 s2 = 0.000841 σ = 0.000529 2 critical values are: 12.401150217
and

18. test statistic = 38.155009452
P-value = 0.0668516983 39.36408 Inferences About 2 Proportions
Two-tailed Proportion (w/ two Ind. Samples)
Given info:
From Sample #1 From Sample #2
x=
56
27
n=
843
703
alpha, α = 0.05 p-bar = 0.053686934
q-bar = 0.946313066
critical values are: -1.959963985 and 1.959964
test statistic = 2.4341272112
P-value = 0.0149277477 Inferences about 2 Means: Independent
Samples
Two-tailed Mean (w/ two Ind. Samples)
Given info:
From Sample #1 From Sample #2
x-bar =
4.2

19. 1.71
n=
22
22
s=
2.2
0.72
alpha, α = 0.05 critical values are: 2.0796138447 and -2.079614
test statistic = 5.0453711835
P-value = 5.38523E-005 find templates you may use in completing
this exam. You will want to highlight
hen input the proper values for the problem you are working on for
quantities One-tailed Proportion
significance level (alpha)
p=
x=
n= 0.01
0.82
56
73 q=
0.18
p-hat = 0.7671232877

20. Left Tailed
Rt. Tailed
critical value is: -2.326347874 or 2.326348
test statistic = -1.175933319
P-value = 0.1198107616 in matched paired two samples)
One-tailed Mean (sigma known)
significance level (alpha)
0.05
x-bar =
24.85
mu, μ =
24
sigma, σ =
2
n=
25
Left Tailed
Rt. Tailed
critical value is: -1.644853627 or 1.644854
test statistic =
2.125

21. P-value = 0.0167933064
One-tailed Mean (sigma unknown)
significance level (alpha)
0.05
x-bar =
110
mu, μ =
118
s=
12
n=
20
Left Tailed
Rt. Tailed
critical value is: -1.729132812 or 1.729133
test statistic = -2.98142397
P-value = 0.0038353067 tion Test
One-tailed Standard Deviation
significance level (alpha)
n= 0.05
25 s=

22. σ= 0.029
0.023 s2 = 0.000841 σ = 0.000529
Left Tailed
Rt. Tailed
critical values are: 13.848425027 or 36.41503
test statistic = 38.155009452
P-value = 0.0334258492
2 One-tailed Proportion (w/ two Ind. Samples)
Given info:
From Sample #1 From Sample #2
x=
50
16
n=
290
123
alpha, α = 0.05 p-bar = 0.1598062954
q-bar = 0.8401937046
critical value is: -1.644853627 or 1.644854
test statistic = 1.0736524347
P-value = 0.1414892436 Samples

23. One-tailed Mean (w/ two Ind. Samples)
Given info:
From Sample #1 From Sample #2
x-bar =
0.94
1.65
n=
21
8
s=
0.31
0.16
alpha, α = 0.05
Right Tail
Left Tail
critical value is: -1.894578605 or 1.894579
test statistic = -8.051464895
P-value = 4.37452E-005