Question Chapter 11 Two Samples Tests of Hypothesis True/False

Chapter 11

Two Samples Tests of Hypothesis

True/False

1. If the null hypothesis states that there is no difference between the mean income of males and the mean income of females, then the test is one-tailed.

Answer:False Difficulty: Easy Goal: 1 AACSB: MD

2. If the null hypothesis states that there is no difference between the mean net income retail stores in Chicago and New York City, then the test is two-tailed.

Answer:True Difficulty: Easy Goal: 1

3. If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.

Answer:True Difficulty: Easy Goal: 1

4. If we are testing for the difference between two population proportions, it is assumed that the two populations are approximately normal and have equal variances.

Answer:False Difficulty: Easy Goal: 2

5. If we are testing for the difference between two population proportions, it is assumed that the two samples are large enough that the binomial distribution can be approximated by the normal distribution.

Answer:True Difficulty: Easy Goal: 2 AACSB: AS

6. When sample sizes are less than 30, a test for the differences between two population means has n–1 degrees of freedom.

Answer:False Difficulty: Easy Goal: 1

7. If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, then the test has (n1 + n2 – 2) degrees of freedom.

Answer:True Difficulty: Easy Goal: 1 AACSB: AS

8. If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the variances are pooled to compute the best estimated variance.

Answer:True Difficulty: Easy Goal: 1

9. If we are testing for the difference between two population means and assume that the two populations have unequal and unknown standard deviations, the degrees of freedom for the test statistic must be computed or calculated.

Answer:True Difficulty: Easy Goal: 1

10. If we are testing for the difference between two population means and assume that the two populations have unequal and unknown standard deviations, the variances are pooled to compute the best estimated variance.

Answer:False Difficulty: Easy Goal: 1 AACSB: REF

11. If samples taken from two populations are not independent, then a test of paired differences is applied.

Answer:True Difficulty: Easy Goal: 3

12. The paired difference test has (n1 + n2 – 2) degrees of freedom.

Answer:False Difficulty: Easy Goal: 3

13. When testing for the difference between two dependent samples, n1 = n2.

Answer:True Difficulty: Easy Goal: 3

14. We use the pooled estimate of the proportion in testing the difference between two population proportions.

Answer:True Difficulty: Medium Goal: 2

15. The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.

Answer:False Difficulty: Medium Goal: 2

16. The paired t test is especially appropriate when the sample sizes of two groups are the same.

Answer:False Difficulty: Easy Goal: 3

17. A committee studying employer-employee relations proposed that each employee would rate his or her immediate supervisor and in turn the supervisor would rate each employee. To find reactions regarding the proposal, 120 office personnel and 160 plant personnel were selected at random. Seventy-eight of the office personnel and 90 of the plant personnel were in favor of the proposal. Computed z = 1.48. At the 0.05 level, it was concluded that there is sufficient evidence to support the belief that the proportion of office personnel in favor of the proposal is greater than that of the plant personnel.

Answer:False Difficulty: Hard Goal: 2

18. A statistics professor wants to compare grades of two different groups of students taking the same course in two different sections. This is an example of a paired sample.

Answer:False Difficulty: Easy Goal: 4

19. In one class, a statistics professor wants to compare grades on the first and second exams. This is an example of paired or dependent observations.

Answer:True Difficulty: Easy Goal: 4

Multiple Choice

20. If the decision is to reject the null hypothesis of no difference between two population parameters, at the 5% level of significance, what are examples of the alternate hypothesis and rejection region?

A) 

B) 

C) 

D) 

Answer:B Difficulty: Hard Goal: 2

21. A poll of 400 people from Dobbs Ferry showed 250 preferred chocolate raspberry coffee while 170 out of 350 in Irvington preferred the same flavor. To test the hypothesis that there is no difference in preferences in the two villages, what is the alternate hypothesis?

A) 

B) 

C) 

D) 

Answer:D Difficulty: Medium Goal: 2

22. If the null hypothesis that two means are equal is true, where will 97% of the computed z-values lie between?

A) 2.58

B) 2.33

C) 2.17

D) 2.07

Answer:C Difficulty: Medium Goal: 1 AACSB: AS

23. How is a pooled estimate of the population proportion represented?

A) pc

B) z

C) 

D) n

Answer:A Difficulty: Medium Goal: 2

24. Suppose we are testing the difference between two proportions at the 0.05 level of significance. If the computed z is –1.07, what is our decision?

A) Reject the null hypothesis

B) Do not reject the null hypothesis

C) Take a larger sample

D) Reserve judgment

Answer:B Difficulty: Medium Goal: 2 AACSB: AS

25. The net weights of a sample of bottles filled by a machine manufactured by Edne, and the net weights of a sample filled by a similar machine manufactured by Orno, Inc., are (in grams):

Edne: 5, 8, 7, 6, 9 and 7

Orno: 8, 10, 7, 11, 9, 12, 14 and 9

Testing the claim at the 0.05 level that the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine, what is the critical value? Assume equal standard deviations for both samples.

A) 2.179

B) 2.145

C) 1.782

D) 1.761

Answer:C Difficulty: Hard Goal: 1

26. A hypothesis will test that two population means are equal. A sample of 10 with a standard deviation of 3 is selected from the first population and a sample of 15 with a standard deviation of 8 from the second population. The standard deviations are not equal. Testing the claim at the 0.01 level, what is the critical value? Assume unequal standard deviations.

A) 2.845

B) 2.787

C) 2.807

D) 2.977

Answer:A Difficulty: Hard Goal: 1

27. Which of the following conditions must be met to conduct a test for the difference in two sample means?

A) Data must be at least of interval scale

B) Populations must be normal

C) Variances in the two populations must be equal

D) A and B correct

E) A, B, and C are correct

Answer:D Difficulty: Medium Goal: 1

28. When is it appropriate to use the paired difference t-test?

A) Four samples are compared at once

B) Any two samples are compared

C) Two independent samples are compared

D) Two dependent samples are compared

Answer:D Difficulty: Medium Goal: 3

29. Using two independent samples, two population means are compared to determine if a difference exists. The population standard deviations are equal. The number in the first sample is fifteen and the number in the second sample is twelve. How many degrees of freedom are associated with the critical value?

A) 24

B) 25

C) 26

D) 27

Answer:B Difficulty: Medium Goal: 1

30. Administering the same test to a group of 15 students and a second group of 15 students to see which group scores higher is an example of

A) a one sample test of means.

B) a two sample test of means.

C) a paired t-test.

D) a test of proportions.

Answer:B Difficulty: Medium Goal: 1 AACSB: AS

31. What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on two samples, both sample sizes are 13? Assume the population standard deviations are equal.

A) 1.708

B) 1.711

C) 2.060

D) 2.064

Answer:B Difficulty: Medium Goal: 1

32. What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on two samples, both sample sizes are 13? The standard deviations for the samples are 5 and 7. Assume the population standard deviations are unequal.

A) 2.064

B) 1.711

C) 2.074

D) 1.717

Answer:D Difficulty: Hard Goal: 1

33. If two samples are used in a hypothesis test for which the combined degrees of freedom is 24, which one of the following is NOT true about the two sample sizes? Assume the population standard deviations are equal.

A) Sample A = 11; sample B = 13

B) Sample A = 12; sample B = 14

C) Sample A = 13; sample B = 13

D) Sample A = 10; sample B = 16

E) Cannot determine from the above information

Answer:A Difficulty: Hard Goal: 1

34. If two samples, one of size 14 and the second of size 13, are used to test the difference between population means, how many degrees of freedom are used to find the critical value? Assume the population standard deviations are equal.

A) 27

B) 26

C) 25

D) 14

E) 13

Answer:C Difficulty: Hard Goal: 1

35. 20 randomly selected statistics students were given 15 multiple-choice questions and 15 open-ended questions – all on the same material. The professor was interested in determining which type of questions the students scored higher. This experiment is an example of

A) a one sample test of means.

B) a two sample test of means.

C) a paired t-test.

D) a test of proportions.

Answer:C Difficulty: Medium Goal: 3

Use the following to answer questions 35-36:

Of 250 adults who tried a new multi-grain cereal, “Wow!”, 187 rated it excellent; of 100 children sampled, 66 rated it excellent.

36. Using the 0.1 significance level and the alternate hypothesisp1 not equal top2, what is the null hypothesis?

A) 

B) 

C) 

D) None of the above

Answer:C Difficulty: Medium Goal: 2

37. What test statistic should we use?

A) z-statistic

B) Right one-tailed test

C) Left one-tailed test

D) Two-tailed test

Answer:A Difficulty: Medium Goal: 2

Use the following to answer questions 38-45:

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is calculated. The results are presented below.

The researcher is interested in determining whether there is evidence that the two processes yield different average errors. Assume that the population standard deviations are equal.

38. What is the null hypothesis?

A) .

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