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.

1. 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

2. 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

3. 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 sample is large.
Chapter 9 Final Review
Classify the hypothesis test as two-tailed, left-tailed, or right-
tailed.
5) In the past, the mean running time for a certain type of
flashlight battery
has been 8.1 hours. The manufacturer has introduced a change

4. in the
production method and wants to perform a hypothesis test to
determine
whether the mean running time has changed as a result.
Classify the conclusion of the hypothesis test as a Type I error,
a Type II error, or a correct decision.
6) The maximum acceptable level of a certain toxic chemical in
vegetables
has been set at 0.2 parts per million (ppm). A consumer health
group
measured the level of the chemical in a random sample of
tomatoes
obtained from one producer to determine whether the mean
level of the
chemical in these tomatoes exceeds the recommended limit.
The hypotheses are
H0 : μ = 0.2 ppm
Ha : μ > 0.2 ppm
where μ is the mean level of the chemical in tomatoes from this
producer.
Suppose that the results of the sampling lead to nonrejection of
the null
hypothesis. Classify that conclusion as a Type I error, a Type II
error, or a
correct decision, if in fact the mean level of the chemical in
these tomatoes
is greater than 0.2 ppm.
Provide an appropriate response.
7) Robert is conducting a hypothesis test concerning a
population mean. The
hypotheses are as follows.
H0 : μ = 50
Ha : μ > 50
He selects a sample of size 35 and finds that the sample mean is

5. 60. He
then does some calculations and finds that for samples of size
35, the
standard deviation of the sample means is 3.2. Do you think that
he
should reject the null hypothesis? Why or why not?
The significance level and P-value of a hypothesis test are
given. Decide whether the null hypothesis
should be rejected.
8) α = 0.01, P-value = 0.002 5
Use a table of t-values to estimate the P-value for the specified
one-mean t-test.
9) Two-tailed test, n = 9, t = 3.696
Provide an appropriate response.
10) A hypothesis test for a population mean is to be performed.
True or false:
The probability of a Type I error is equal to the significance
level.
CHAPTER 9 Answers
5) Two-tailed
6) Type II error
7) Answers will vary. Possible answer. Yes, he should reject the
null hypothesis. If H0 were true, it is
not very likely that the sample mean would be as big as 60,
since this is more than three standard
deviations from 50. So the observed sample mean is inconsistent

6. with the null hypothesis.
8) Reject the null hypothesis.
9) P < 0.01
10) True
Chapter 10 Final Review.
Summary statistics are given for independent simple random
samples from two populations. Use the
pooled t-interval procedure to obtain the specified confidence
interval.
11) x1 = 12.8, s1 = 4.1, n1 = 14, x2 = 17.4, s2 = 4.8, n2 = 17
Determine a 95% confidence interval.
Summary statistics are given for independent simple random
samples from two populations. Use the
pooled t-test to conduct the required hypothesis test.
12) x1 = 12.5, s1 = 4.1, n1 = 14, x2 = 16.9, s2 = 4.6, n2 = 17
Perform a two-tailed hypothesis test using a significance level
of α = 0.05.
Provide an appropriate response.
13) In comparing the means of two populations, some methods
are based on
independent samples and some are based on paired samples.
Explain the
difference between independent and paired samples. Give an
example of
each type of sample.

7. CHAPTER 10 Answers
11) -7.92 to -1.28
12) Test statistic: t = -2.782
Critical value = ±2.045
Reject H 0
13) In paired samples, there is a natural pairing of the members
of the two populations. In independent
samples, no such pairing exists. An example of an independent
sample is the income of men and
women. An example of a paired sample is the income of
husbands and their wives. (Examples will
vary.)
Chapter 12 Final Review
Use the chi-square table to find the required χ2-value(s).
14) For a χ2-curve with 23 degrees of freedom, find the χ2-
value having
area 0.995 to its right.
15) For a χ2-curve with df = 5, determine χ 2
0.995.
Perform the required chi-square hypothesis test. Preliminary
data analyses and other information
indicate that it is reasonable to assume that the variable under
consideration is normally distributed.

8. Use the critical-value approach or the P-value approach as
indicated.
16) In 2000, the standard deviation of the scores of all students
taking a
particular test was 20.3. In 2005, the standard deviation of the
scores of a
random sample of 18 students taking the same test was s = 27.1.
At the
5% level of significance, do the data provide sufficient evidence
to
conclude that the standard deviation, σ, of all 2005 scores is
different
from the 2000 standard deviation of 20.3? Use the P-value
approach.
CHAPTER 12 Answers
14) 9.260
15) 0.412
16) H0: σ = 20.3 Ha: σ ≠ 20.3
α = 0.05
Test statistic: χ2 = 30.297
0.02 < P < 0.05
Reject the null hypothesis. At the 5% level of significance, the
data provide sufficient evidence to
conclude that the standard deviation, σ, of all 2005 scores is
different from 20.3.
Chapter 13 Final Review
Find the required F-value.
17) An F-curve has df = (30, 12). Find the F-value having area
0.01 to its

9. right.
Provide an appropriate response.
18) True or false: In a one-way ANOVA, if the null hypothesis
is rejected, we
conclude that the population means are all different (i.e., no two
of the
population means are equal).
Preliminary data analyses indicate that it is reasonable to
consider the assumptions for one -way
ANOVA satisfied. Perform the required hypothesis test using
the critical value approach.
19) At the 0.025 significance level, do the data provide
sufficient evidence to
conclude that a difference exists between the population means
of the
four different brands? The sample data are given below. Use
One-Way ANOVA.xls. Click Enable Editing and change values
to match values in this problem. One-Way ANOVA.xls
Chapter 13 Answers
17) 3.70
18) False
19) H0: μ1 = μ = μ3 = μ4. Ha: Not all the means are equal.
Test statistic: F = 0.0555. Critical value: F = 3.95.

10. Fail to reject the null hypothesis. There is not sufficient
evidence to conclude that a difference exists
between the population means of the four different brands.
Chapter 14 Final Review
20)The sample data below are the typing speeds (in words per
minute) and
reading speeds (in words per minute) of nine randomly selected
secretaries. Here, x denotes typing speed, and y denotes reading
speed.
Use the data to predict the reading speed of a secretary whose
typing
speed is 48. In other words, find the regression line, let x = 48
and find the predicted y. Round your answer to the nearest
word per minute.
Provide an appropriate response.
21) The correlation test for normality involves computing the
linear correlation
coefficient between which of the following pairs?
A) The sample data and the population data
B) The predictor variable and the response variable
C) The values of the response variable and their normal scores
D) The sample data and their normal scores

11. CHAPTER 14 Answers
Test statistic: R p = 0.932
Critical value: R *
p = 0.935
Reject H 0 . At the 10% significance level, the data provide
sufficient evidence to conclude that
weekly salaries of employees at this company are not normally
distributed.
20) 458 words per minute
21) D