Bus Stat Test 3 Practice Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. The level of significance
a. can be any positive value
b. can be any value
c. is (1 - confidence level)
d. can be any value between -1.96 to 1.96
____ 2. The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles.
Management believes that due to a new production process, the life expectancy of their tires has increased. In
order to test the validity of their belief, the correct set of hypotheses is
a. H0:  < 40,000 Ha:   40,000
b. H0:   40,000 Ha:  > 40,000
c. H0:  > 40,000 Ha:   40,000
d. H0:   40,000 Ha:  < 40,000
Exhibit 9-1

n = 36 = 24.6 S = 12 H0:   20
Ha:  > 20
____ 3. Refer to Exhibit 9-1. If the test is done at 95% confidence, the null hypothesis should
a. not be rejected
b. be rejected
c. Not enough information is given to answer this question.
d. None of these alternatives is correct.
Exhibit 9-3

n = 49 = 54.8 s = 28 H0:  = 50
Ha:   50
____ 4. Refer to Exhibit 9-3. The p-value is equal to
a. 0.1151
b. 0.3849
c. 0.2698
d. 0.2302
____ 5. Refer to Exhibit 9-3. If the test is done at the 5% level of significance, the null hypothesis should
a. not be rejected
b. be rejected
c. Not enough information given to answer this question.
d. None of these alternatives is correct.

Exhibit 9-4
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it
took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We
want to test to determine whether or not the mean waiting time of all customers is significantly more than 3
minutes.
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____ 6. Refer to Exhibit 9-4. The standardized test statistic is
a. 1.96
b. 1.64
c. 2.00
d. 0.056
____ 7. For a two-tailed test at 86.12% confidence, Z =
a. 1.96
b. 1.48
c. 1.09
d. 0.86
____ 8. For a one-tailed test (upper tail), a sample size of 18 at 95% confidence, t =
a. 2.12
b. -2.12
c. -1.740
d. 1.740
Exhibit 9-6
A random sample of 16 students selected from the student body of a large university had an average age of 25
years and a standard deviation of 2 years. We want to determine if the average age of all the students at the
university is significantly different from 24. Assume the distribution of the population of ages is normal.
____ 9. Refer to Exhibit 9-6. At 95% confidence, it can be concluded that the mean age is
a. not significantly different from 24
b. significantly different from 24
c. significantly less than 24
d. significantly less than 25
____ 10. For a one-tailed test (lower tail) at 89.8% confidence, Z =
a. -1.27
b. -1.53
c. -1.96
d. -1.64
____ 11. For a one-tailed test (upper tail), a sample size of 26 at 90% confidence, t =
a. 1.316
b. -1.316
c. -1.740
d. 1.740
____ 12. For a one-tailed test (lower tail), a sample size of 22 at 95% confidence, t =
a. -1.383
b. 1.383
c. -1.717
d. -1.721

____ 13. Which of the following statements is not a required assumption for developing an interval estimate of the
difference between two sample means when the samples are small?
a. Both populations have normal distributions.
b. 1 = 2 = 1
c. Independent random samples are selected from the two populations.
d. The variances of the two populations are equal.
____ 14. If we are interested in testing whether the mean of population 1 is smaller than the mean of population 2, the
a. null hypothesis should state 1 - 2 < 0
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 b. null hypothesis should state 1 - 2 > 0
c. alternative hypothesis should state 1 - 2  0
d. alternative hypothesis should state 1 - 2  0
____ 15. If we are interested in testing whether the mean of population 1 is larger than the mean of population 2, the
a. null hypothesis should state 1 - 2 < 0
b. null hypothesis should state 1 - 2  0
c. alternative hypothesis should state 1 - 2  0
d. alternative hypothesis should state 1 - 2  0
Exhibit 10-1
Salary information for a random sample of male and female employees of a large company is shown below.

Male Female
Sample Size 64 36
Sample Mean Salary (in $1,000) 44 41
Sample Variance 128 72
____ 16. Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations is
a. -28
b. 3
c. 4
d. -4
____ 17. Refer to Exhibit 10-1. The p-value is
a. 0.0668
b. 0.0334
c. 1.336
d. 1.96

Exhibit 10-2
The following information was obtained from matched samples.
The daily production rates for a sample of workers before and after a training program are shown below.

Worker Before After

1 20 22
2 25 23
3 27 27
4 23 20
5 22 25
6 20 19
7 17 18
____ 18. Refer to Exhibit 10-2. The point estimate for the difference between the means of the two populations is
a. -1
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 b. -2
c. 0
d. 1
Exhibit 10-3
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today
and those enrolled five years ago. A sample of final examination scores from students enrolled today and from
students enrolled five years ago was taken. You are given the following results.

Today Five Years Ago

Mean 82 88
Variance 112.5 54
Sample Size 45 36
____ 19. Refer to Exhibit 10-3. The p-value for the difference between the two population means is
a. .0014
b. .0028
c. .4986
d. .9972
Exhibit 10-6
The management of a department store is interested in estimating the difference between the mean credit
purchases of customers using the store's credit card versus those customers using a national major credit card.
Independent samples of credit sales are shown below.

Store's Card Major Credit Card

Sample size 64 49
Sample mean $140 $125
Sample standard deviation $10 $8

____ 20. Refer to Exhibit 10-6. A point estimate for the difference between the mean purchases of the users of the two
credit cards is
a. 2
b. 18
c. 265
d. 15
Exhibit 10-7
In order to estimate the difference between the average daily sales of two branches of a department store, the
following data has been gathered. Assume the two populations are normally distributed and have equal
variances.

Downtown Store North Mall Store

Sample size 12 days 14 days
Sample mean $36,000 $32,000
Sample standard deviation $1,200 $1,000
____ 21. Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is
a. 3109.90 to 4890.10
b. 32000 to 36000
c. 12 to 14

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 d. 1000 to 1200
Exhibit 10-9
Two major automobile manufacturers have produced compact cars with the same size engines. We are
interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the
two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight
drivers are selected to drive each automobile for a specified distance. The following data show the results of
the test.

Driver Manufacturer A Manufacturer B

1 29 27
2 24 23
3 26 28
4 24 23
5 25 24
6 27 26
7 30 28
8 25 27
____ 22. Refer to Exhibit 10-9. The mean for the differences is
a. 0.50
b. 1.25
c. 18
d. 0.000

____ 23. In an analysis of variance where the total sample size for the experiment is n and the number of populations is
p, the mean square within treatments is
a. SSE/(n - p)
b. SSTR/(n - p)
c. SSE/(p - 1)
d. SSE/p
____ 24. The ANOVA procedure is a statistical approach for determining whether or not
a. the means of two samples are equal
b. the means of two or more samples are equal
c. the means of more than two samples are equal
d. the means of two or more populations are equal
Exhibit 10-10

SST = 6,750 H0: 1=2=3=4

SSE = 8,000 Ha: at least one mean is different
n = 20
____ 25. Refer to Exhibit 10-10. The null hypothesis is to be tested at the 5% level of significance. The critical value
from the table is
a. 2.87
b. 3.24
c. 4.08
d. 8.7
Exhibit 10-12
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 Part of an ANOVA table is shown below.

Source of Sum of Degrees of Mean

Variation Squares Freedom Square F

Treatments 180 3

Error
(within
treatments)

TOTAL 480 18
____ 26. Refer to Exhibit 10-12. The mean square within treatments (MSE) is
a. 60
b. 15
c. 300
d. 20

Exhibit 10-13
Part of an ANOVA table is shown below.

Source of Sum of Degrees Mean

Variation Squares of Freedom Square F
Treatments 64 8

Error 2

Total 100
____ 27. Refer to Exhibit 10-13. The number of degrees of freedom corresponding to between treatments is
a. 18
b. 2
c. 4
d. 3
Exhibit 10-14
The following is part of an ANOVA table which was the results of three treatments and a total of 15
observations.

Source of Sum of Degrees of

Variation Squares Freedom
Between
Treatments 64

Error (Within
Treatments) 96
____ 28. Refer to Exhibit 10-14. The computed test statistics is
a. 32

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 b. 8
c. 0.667
d. 4
Exhibit 11-1
In a random sample of 60 men, 42 reported that they were in favor of team A to win the Superbowl, while in a
sample of 100 women 77 favored team A to win.
____ 29. Refer to Exhibit 11-1. The 95% confidence interval for the difference between the proportions of the two
populations is
a. - 0.07 to 0
b. - 0.212 to 0.072
c. -1.96 to 1.96
d. 0.70 to 0.77

Short Answer Problems

1. From a population of cans of coffee marked "12 ounces," a sample of 25 cans is selected and the contents of each can
are weighed. The sample revealed a mean of 11.8 ounces with a standard deviation of 0.5 ounces. Test to see if the mean
of the population is at least 12 ounces. (Assume the population is normally distributed.) Use a .05 level of significance.
At a minimum state your hypotheses, give me the critical value, calculate your test stat, and give me the conclusion.

2. Consider the following hypothesis test:

Ho:   38
Ha:  > 38

You are given the following information obtained from a random sample of six observations. X = { 38,40, 42, 32, 46, 42}

a.Compute the mean of the sample

b.Determine the standard deviation of the sample.
c.Using α = 0.05, what is the rejection rule?
d.Determine the standard error of the mean.
e.Compute the value of the test statistic. What is your conclusion?

3.Part of an ANOVA table involving 8 groups for a study is shown below.

Source of Variation Sum of Squares Degrees of Freedom Mean Square F-Stat

Treatments 126 ? ? ?

Error 240 ? ?

Total ? 67

a.Complete all the missing values in the above table and fill in the blanks.
b.Use α = 0.01 to determine if there is any significant difference among the means of the eight groups. At a minimum
state your hypotheses, give me the critical value, calculate your test stat, and give me the conclusion.

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4. MNM, Inc. has three stores located in three different areas. Random samples of the daily sales of the three stores (in
$1,000) are shown below. At 95% confidence, test to see if there is a significant difference in the average sales of the
three stores. At a minimum state your hypotheses, give me the critical value, calculate your test stat, and give me the
conclusion.

Store 1 Store 2 Store 3

9 10 6
8 11 7
7 10 8
8 13 11

5. Consider the following hypothesis test:

Ho: p = 0.5
Ha: p  0.5

A sample of 800 provided a sample proportion of 0.58.

a. Using  = 0.05, what is the rejection rule?

b. Determine the standard error of the proportion.
c. Compute the value of the test statistic z. What is your conclusion?
d. Determine the p-value.

6. A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated
they like the taste.
a. At a 5% significance level, test to determine if at least 22% of the population will like the new soft drink. At a
minimum state your hypotheses, give me the critical value, calculate your test stat, and give me the conclusion.

b. Determine the p-value.

7. The business manager of a local health clinic is interested in estimating the difference between the fees for extended
office visits in her center and the fees of a newly opened group practice. She gathered the following information
regarding the two offices.

Health Clinic Group Practice

Sample size 50 visits 45 visits
Sample mean $21 $19
Standard deviation $2.75 $3.00

a. Develop an interval estimate for the difference between the average fees of the two offices. Use a confidence
coefficient of 0.95.
b. Test to see if there is a difference between the two means at the 95% confidence level. At a minimum state your
hypotheses, give me the critical value, calculate your test stat, and give me the conclusion.

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