Deck 10: Two-Sample Tests of Hypothesis

Question 1

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) Populations must be normal, the variances must be equal and the two samples must be unrelated, that is, independent.

Answer 1

Populations must be normal, the variances must be equal and the two samples must be unrelated, that is, independent.

Question 2

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 2

a two sample test of means.

Question 3

Using two independent samples, two population means are compared to determine if a difference exists. 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 3

25

Question 4

If two samples are used in a hypothesis test for which the combined degrees of freedom is 24, which one of the following CANNOT be true about the two sample sizes?

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

Question 5

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

A) $\pm$ 2.58
B) $\pm$ 2.33
C) $\pm$ 2.17
D) $\pm$ 2.07

Question 6

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.
What is the null hypothesis?

A) µ_A - µ_B = 0
B) µ_A - µ_B $\neq$ 0
C) µ_A - µ_B $\le$ 0
D) µ_A - µ_B > 0

Question 7

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.
What is the computed value of t?

A) +2.797
B) -2.797
C) -13.905
D) +13.70

Question 8

If two samples are used in a hypothesis test for which the combined degrees of freedom is 27, which one of the following might be true about the two sample sizes?

A) Sample A = 14; Sample B = 13
B) Sample A = 12; Sample B = 13
C) Sample A = 15; Sample B = 14
D) Sample A = 20; Sample B = 8

Question 9

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.
What is the critical t value at the 1% level of significance?

A) +2.779
B) -2.492
C) $\pm$ 1.711
D) $\pm$ 2.797

Question 10

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.
Ball Bearings
Hypothesis Test: Independent Groups (t-test, pooled variance)
What is the decision at the 1% level of significance?

A) Reject the null hypothesis and conclude the means are different.
B) Reject the null hypothesis and conclude the means are the same.
C) Fail to reject the null hypothesis and conclude the means are the same.
D) Fail to reject the null hypothesis and conclude the means are different.

Question 11

i. 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. ii. 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.
iii. If we are testing for the difference between two population means, it is assumed that the two populations are approximately normal and have equal variances.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 12

i. 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. ii. 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.
iii. The critical value for the claim that the difference of two means is less than zero with a level of significance of 0.025 and sample sizes of nine and seven, is -2.179.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 13

i. 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. ii. If we are testing for the difference between two population means, it is assumed that the two populations are approximately normal and have equal variances.
iii. The critical value of t for a two-tail test of the difference of two means, a level of significance of 0.10 and sample sizes of seven and fifteen, is $\pm$ 1.734.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 14

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.
What is the alternate hypothesis?

A) µ_A - µ_B = 0
B) µ_A - µ_B $\neq$ 0
C) µ_A - µ_B $\le$ 0
D) µ_A - µ_B > 0

Question 15

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

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 16

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.
There are how many degrees of freedom?

A) 10
B) 13
C) 26
D) 24

Question 17

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. Given the following MegaStat printout, what analysis and decision can be made?

A) Reject the null hypothesis and conclude the means are different.
B) Reject the null hypothesis and conclude the means are the same.
C) Fail to reject the null hypothesis at the 1% level of significance.
D) Fail to reject the null hypothesis at the 5% level of significance and conclude the means are different.

Question 18

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): Testing the claim at the 0.05 level 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?

A) -1.96
B) -2.837
C) -6.271
D) +3.674
E) +1.782

Question 19

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?

A) 1.708
B) 1.711
C) 2.060
D) 2.064

Question 20

i. 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. ii. If we are testing for the difference between two population means, it is assumed that the two populations are approximately normal and have equal variances.
iii. When sample sizes are less than 30, a test for the differences between two population means has n - 1 degrees of freedom.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 21

A poll of 400 people from village 1 showed 250 preferred chocolate raspberry coffee to the regular blend while 170 out of 350 in village 2 preferred the same flavour. To test the hypothesis that there is no difference in preferences in the two villages, what is the alternate hypothesis?

A) p₁ - p₂ < 0
B) p₁ - p₂ > 0
C) p₁ = p₂
D) p₁ - p₂ $\neq$ 0

Question 22

How is a pooled estimate represented?

A) p_c
B) z
C) p
D) np

Question 23

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.
What is the decision at the 1% level of significance?

A) Reject the null hypothesis and conclude the means are different.
B) Reject the null hypothesis and conclude the means are the same.
C) Fail to reject the null hypothesis and conclude the means are the same.
D) Fail to reject the null hypothesis and conclude the means are different.

Question 24

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions?
i. The null hypothesis is p_a - p_b = 0.
ii. The alternate hypothesis is p_a - p_b $\neq$ 0.
iii. The proportion of sales made in Market Area 2 is 0.33.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 25

i. 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 favour 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 favour of the proposal is greater than that of the plant personnel. ii. We use the pooled estimate of the proportion in testing the difference between two population proportions.
iii. The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.

A) (i), (ii), and (iii) are all false statements.
B) (ii) is a correct statement but not (i) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i) is a correct statement but not (ii) and (iii).

Question 26

i. We use the pooled estimate of the proportion in testing the difference between two population proportions when the samples are not chosen independently. ii. The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.
iii. 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 favour 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 favour of the proposal is greater than that of the plant personnel.

A) (i), (ii), and (iii) are all false statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i) is a correct statement, but not (ii) and (iii).

Question 27

The results of a mathematics placement exam at Mercy College for two campuses are as follows:
What is the null hypothesis if we want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2?

A) µ₁ = 0
B) µ₂ = 0
C) µ₁ = µ₂
D) µ₁ > µ₂
E) µ₁ - µ₂ $\le$ 0

Question 28

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions?
i. The null hypothesis is p_a - p_b > 0.
ii. The alternate hypothesis is p_a - p_b $\neq$ 0.
iii. The pooled estimate of the population proportion is 0.36.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 29

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.

Question 30

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions? i. The null hypothesis is p_a - p_b = 0.
ii. The alternate hypothesis is p_a - p_b > 0.
iii. The z-statistic is 3.40.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 31

The results of a mathematics placement exam at Mercy College for two campuses are as follows: What is the p-value if the computed test statistic is 4.1?

A) 1.0
B) 0.0
C) 0.05
D) 0.95

Question 32

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions?
i. The alternate hypothesis is p_a - p_b $\neq$ 0.
ii. The pooled estimate of the population proportion is 0.36.
iii. Using the 1% level of significance, the critical value is $\pm$ 1.96.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 33

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions?
i. The null hypothesis is p_a - p_b = 0.
ii. The alternate hypothesis is p_a - p_b $\neq$ 0.
iii. The proportion of sales made in Market Area 1 is 0.45.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 34

If the decision is to reject the null hypothesis at the 5% level of significance, what are the acceptable alternate hypothesis and rejection region?

A) p₁ $\neq$ p₂; z > 1.65 and z < -1.65
B) p₁ $\neq$ p₂; z > 1.96 and z < -1.96
C) p₁ > p₂; z < -1.65
D) p₁ > p₂; z < -1.96

Question 35

The results of a mathematics placement exam at Mercy College for two campuses are as follows: What is the computed value of the test statistic?

A) 9.3
B) 2.6
C) 3.4
D) 1.9

Question 36

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions?
i. The null hypothesis is p_a - p_b = 0.
ii. The alternate hypothesis is p_a - p_b $\neq$ 0.
iii. If $\alpha$ = 0.01 and the z-statistic were calculated to be -1.96, your decision would be to fail to reject.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 37

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 calculated t to be +2.70; what is the decision at the 0.01 level of significance?

A) Reject the null hypothesis and conclude the means are different.
B) Reject the null hypothesis and conclude the means are the same.
C) Fail to reject the null hypothesis and conclude the means are the same.
D) Fail to reject the null hypothesis and conclude the means are different.

Question 38

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions?
i. The alternate hypothesis is p_a - p_b $\neq$ 0.
ii. The proportion of sales made in Market Area 1 is 0.40.
iii. The proportion of sales made in Market Area 2 is 0.33.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 39

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.
This example is what type of test?

A) One sample test of means.
B) Two sample test of means.
C) Paired t-test.
D) Test of proportions.

Question 40

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions?
i. The null hypothesis is p_a - p_b = 0.
ii. The alternate hypothesis is p_a - p_b $\neq$ 0.
iii. Using the 1% level of significance, the critical value is $\pm$ 2.58.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 41

A recent study compared the time spent together by single and dual-earner couples. According to the records kept during the study, the mean amount of time spent together watching TV among single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean time was 48.4 and the standard deviation was 18.1. At a 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching TV together? There were 15 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.

A) Reject if t > 2.485, t = 1.91, insufficient evidence to say that single-earner couples spend more time watching TV together.
B) Reject if t > 2.485, t = 2.11, insufficient evidence to say that single-earner couples spend more time watching TV together.
C) Reject if t > 2.473, t = 1.95, insufficient evidence to say that single-earner couples spend more time watching TV together.
D) Reject if t > 2.473, t = 2.55, single-earner couples spend more time watching TV together.
E) Reject if t > 2.485, t = 2.55, single-earner couples spend more time watching TV together.

Question 42

A recent study compared the time spent together by single and dual-earner couples. According to the records kept during the study, the mean amount of time spent together watching TV among single-earner couples was 60 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean time was 48.4 and the standard deviation was 18.1. At a 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching TV together? There were 12 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.

A) Reject if t > 2.485, t = 2.77, single-earner couples spend more time watching TV together.
B) Reject if t > 2.508, t = 1.96, insufficient evidence to say that single-earner couples spend more time watching TV together.
C) Reject if t > 2.797, t = 2.57, single-earner couples spend more time watching TV together.
D) Reject if t > 2.508, t = 1.69, insufficient evidence to say that single-earner couples spend more time watching TV together.
E) Reject if t > 2.508, t = 0.96, insufficient evidence to say that single-earner couples spend more time watching TV together.

Question 43

i. If samples taken from two populations are not independent, then a test of paired differences is applied. ii. The paired difference test has (n₁ + n₂ - 2) degrees of freedom.
iii. The paired t test is especially appropriate when the sample sizes of two groups are the same.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i) is a correct statement but not (ii) and (iii).

Question 44

Of 250 adults who tried a new multi-grain cereal, Wow!, 187 rated it excellent; of 100 children sampled, 66 rated it excellent. What test statistic should we use?

A) z-statistic
B) Right one-tailed test
C) Left one-tailed test
D) Two-tailed test

Question 45

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions?
i. Using the 1% level of significance, the critical value is $\pm$ 2.58.
ii. The z-statistic is 3.40.
iii. Your decision is to reject the null hypothesis.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 46

Of 150 adults who tried a new peach-flavoured peppermint patty, 99 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the 0.10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flavour as excellent? State the decision rule, the value of the test statistic, and your decision.

A) Reject if z > 1.96 or < -1.96, z = -2.26, difference exists.
B) Reject if z > 1.96 or < -1.96, z = -0.66, no difference.
C) Reject if z > 1.645 or < -1.645, z = 0.87, difference exists.
D) Reject if z > 1.645 or < -1.645, z = -0.28, difference exists.
E) Reject if z > 1.645 or < -1.645, z = 0.87, no difference.

Question 47

i. The paired difference test has (n₁ + n₂ - 2) degrees of freedom. ii. The paired t test is especially appropriate when the sample sizes of two groups are the same.
iii. 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.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 48

Of 150 adults who tried a new peach-flavoured peppermint patty, 87 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the 0.10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flavour as excellent? State the decision rule, the value of the test statistic, and your decision.

A) Reject if z > 1.645 or < -1.645, z = -0.66, no difference.
B) Reject if z > 1.645, z = -0.66, no difference.
C) Reject if z > 1.645 or < -1.645, z = -5.28, difference exists.
D) Reject if z > 1.96 or < -1.96, z = -0.66, no difference.
E) Reject if z > 1.96 or < -1.96, z = -2.26, difference exists.

Question 49

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions?
i. The alternate hypothesis is p_a - p_b $\neq$ 0.
ii. Using the 1% level of significance, the critical value is $\pm$ 2.58.
iii. The z-statistic is 3.40.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 50

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.

Question 51

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions? i. The alternate hypothesis is p_a - p_b > 0.
ii. The z-statistic is 3.40.
iii. Your decision is to accept the null hypothesis.

A) (i), (ii), and (iii) are all correct statements
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 52

A recent study compared the time spent together by single and dual-earner couples. According to the records kept during the study, the mean amount of time spent together watching TV among single-earner couples was 64 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean time was 48.4 and the standard deviation was 18.1. At a 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching TV together? There were 20 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.

A) Reject if t > 2.457, t = 2.49, single-earner couples spend more time watching TV together.
B) Reject if t > 2.508, t = 0.96, insufficient evidence to say that single-earner couples spend more time watching TV together.
C) Reject if t > 2.797, t = 2.57, single-earner couples spend more time watching TV together.
D) Reject if t > 2.042, t = 1.96, insufficient evidence to say that single-earner couples spend more time watching TV together.
E) Reject if t > 2.485, t = 2.77, single-earner couples spend more time watching TV together.

Question 53

Of 150 adults who tried a new peach-flavoured peppermint patty, 81 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the 0.10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flavour as excellent? State the decision rule, the value of the test statistic, and your decision.

A) Reject if z > 1.645 or < -1.645, z = -1.28, no difference.
B) Reject if z > 1.645 or < -1.645, z = -1.28, difference exists.
C) Reject if z > 1.96 or < -1.96, z = -0.66, no difference.
D) Reject if z > 1.96 or < -1.96, z = -1.41, difference exists.
E) Reject if z > 1.645 or < -1.645, z = -1.41, no difference.

Question 54

i. If samples taken from two populations are not independent, then a test of paired differences is applied. ii. The paired difference test has (n₁ + n₂ - 2) degrees of freedom.
iii. 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.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) is a correct statement but not (ii) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 55

A recent study compared the time spent together by single and dual-earner couples. According to the records kept during the study, the mean amount of time spent together watching TV among single-earner couples was 55 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean time was 48.4 and the standard deviation was 18.1. At a 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching TV together? There were 12 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.

A) Reject if t > 2.485, t = 2.57, insufficient evidence to say that single-earner couples spend more time watching TV together.
B) Reject if t > 2.508, t = 0.96, insufficient evidence to say that single-earner couples spend more time watching TV together.
C) Reject if t > 2.473, t = 2.57, single-earner couples spend more time watching TV together.
D) Reject if t > 2.508, t = 0.96, single-earner couples spend more time watching TV together.
E) Reject if t > 2.485, t = 2.01, single-earner couples spend more time watching TV together.

Question 56

A recent study compared the time spent together by single and dual-earner couples. According to the records kept during the study, the mean amount of time spent together watching TV among single-earner couples was 65 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean time was 48.4 and the standard deviation was 18.1. At a 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching TV together? There were 15 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.

A) Reject if t > 2.485, t = 2.01, single-earner couples spend more time watching TV together.
B) Reject if t > 2.473, t = 1.95, insufficient evidence to say that single-earner couples spend more time watching TV together.
C) Reject if t > 2.473, t = 2.57, single-earner couples spend more time watching TV together.
D) Reject if t > 2.485, t = 2.57, insufficient evidence to say that single-earner couples spend more time watching TV together.
E) Reject if t > 2.485, t = 2.52, single-earner couples spend more time watching TV together.

Question 57

Of 150 adults who tried a new peach-flavoured peppermint patty, 90 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the 0.10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flavour as excellent? State the decision rule, the value of the test statistic, and your decision.

A) Reject if z > 1.645 or < -1.645, z = -0.28, difference exists
B) Reject if z > 1.645 or < -1.645, z = -0.28, no difference.
C) Reject if z > 1.645 or < -1.645, z = -1.28, difference exists.
D) Reject if z > 1.96 or < -1.96, z = -0.66, no difference.
E) Reject if z > 1.96 or < -1.96, z = -2.26, difference exists.

Question 58

Of 250 adults who tried a new multi-grain cereal, Wow! 187 rated it excellent; of 100 children sampled, 66 rated it excellent. Using the 0.1 significance level and the alternate hypothesisp₁not equal top₂, what is the null hypothesis?

A) p₁ - p₂ > 0
B) p₁ - p₂ < 0
C) p₁ - p₂ = 0

Question 59

i. If samples taken from two populations are not independent, then a test of paired differences is applied. ii. The paired difference test has (n - 1) degrees of freedom.
iii. The paired t test is especially appropriate when the sample sizes of two groups are the same.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (ii) is a correct statement but not (i) and (iii).

Question 60

Of 150 adults who tried a new peach-flavoured peppermint patty, 75 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the 0.10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flavour as excellent? State the decision rule, the value of the test statistic, and your decision.

A) Reject if z > 1.645, z = -0.66, no difference.
B) Reject if z > 1.645 or < -1.645, z = -5.28, difference exists.
C) Reject if z > 1.96 or < -1.96, z = -2.15 no difference.
D) Reject if z > 1.96 or < -1.96, z = -2.26, difference exists.
E) Reject if z > 1.645 or < -1.645, z = -2.15, difference exists.

Question 61

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $1000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? What is the decision at the 5% level of significance?

A) Looking at the large P-value of.2019 we conclude LIFO is more effective.
B) Reject the null hypothesis and conclude LIFO is more effective.
C) Reject the alternate hypothesis and conclude LIFO is more effective.
D) The large P-value of.2017 indicates that there is a good chance of getting this sample data when the two methods are in fact not significantly different, so we conclude that LIFO is not more effective.

Question 62

The employees at the East Vancouver office of a multinational company are demanding higher salaries than those offered at the company office located in Oshawa Ontario. Their justification for the pay difference is that the difference between the average price of single-family houses in East Vancouver and that in Oshawa is more than $60,000. Before making a decision, the company management wants to study the difference in the prices of single-family houses for sale at the two locations. The results of their search of recent house sales are as follows (in $1000, rounded to the nearest thousand):
Assuming that the population distributions are approximately normal, can we conclude at the 0.05 significance level that the difference between the two population means is greater than $60,000?
What is the degree of freedom?

A) 4
B) 5
C) 15
D) 23
E) 9

Question 63

Married women are more often than not working outside the home on at least a part-time basis, as do most mannered men. Does a husband's employment status affect his wife's well-being? In an attempt to answer this question, 75 married female professionals were surveyed as to their job satisfaction. In this sample, 45 husbands were employed, and 30 were unemployed. The Learning Objective of the study was to compare the mean job satisfaction levels of the married women with working husbands, with the mean job satisfaction levels of the married women with husbands that stayed at home. The test statistic for this problem has what type of distribution?

A) Normal z
B) Student's t
C) Positively skewed
D) Negatively skewed
E) Binomial

Question 64

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $1000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? What is the degree of freedom?

A) 4
B) 5
C) 15
D) 10
E) 9

Question 65

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $1000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?
If you use the 5% level of significance, what is the critical t value?

A) +2.571
B) $\pm$ 2.776
C) +2.262
D) $\pm$ 2.228
E) +2.132

Question 66

A random sample of 20 statistics students was 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.

Question 67

Married women are more often than not working outside the home on at least a part-time basis, as do most mannered men. Does a husband's employment status affect his wife's well-being? In an attempt to answer this question, 75 married female professionals were surveyed as to their job satisfaction. In this sample, 45 husbands were employed, and 30 were unemployed. The Learning Objective of the study was to compare the mean job satisfaction levels of the married women with working husbands, with the mean job satisfaction levels of the married women with husbands that stayed at home. If you were to use Excel's Data Analysis to assist in your solution to this problem, which test would you use?

A) T-test: paired 2-sample for means.
B) T-test: 2-sample assuming equal variances.
C) T-test: 2-sample assuming unequal variances.
D) Z-test: 2-sample for means.
E) F-test: 2-sample for variances.

Question 68

A local retail business wishes to determine if there is a difference in preferred indoor temperature between men and women. A random sample of data is collected, with the following results: What is the decision at the 5% level of significance?

A) Since the p-value is large at 0.4752, we fail to reject the null hypothesis and conclude that there is no significant difference in the preferred room temperatures between the sexes.
B) Since the p-value is small at 0.4752, we reject the null hypothesis and conclude that there is a significant difference in the preferred room temperatures between the sexes.
C) Since the calculated t-value is more than the critical t-value, we reject the null hypothesis and conclude that there is a significant difference in the preferred room temperatures between the sexes.
D) Since the calculated t-value is more than the critical t-value, we fail to reject the null hypothesis and conclude that there is a significant difference in the preferred room temperatures between the sexes.
E) There is insufficient information to make a decision.

Question 69

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $1000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?
What is the null hypothesis?

A) µ_F = µ_L, or µ_d = 0
B) µ_F $\neq$ µ_L, or µ_d $\neq$ 0
C) µ_F $\le$ µ_L
D) µ_F > µ_L

Question 70

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $1000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? What is the decision at the 5% level of significance?

A) Fail to reject the null hypothesis and conclude LIFO is more effective.
B) Reject the null hypothesis and conclude LIFO is more effective.
C) Reject the alternate hypothesis and conclude LIFO is more effective.
D) Fail to reject the null hypothesis and conclude LIFO is not more effective.

Question 71

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $1000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?
What is the alternate hypothesis?

A) µ_F = µ_L, or µ_d = 0
B) µ_F $\neq$ µ_L, or µ_d $\neq$ 0
C) µ_F $\le$ µ_L
D) µ_F > µ_L

Question 72

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $1000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?
What is the value of calculated t?

A) +0.93
B) $\pm$ 2.776
C) +0.0.47
D) -2.028

Question 73

The employees at the East Vancouver office of a multinational company are demanding higher salaries than those offered at the company office located in Oshawa Ontario. Their justification for the pay difference is that the difference between the average price of single-family houses in East Vancouver and that in Oshawa is more than $60,000. Before making a decision, the company management wants to study the difference in the prices of single-family houses for sale at the two locations. The results of their search of recent house sales are as follows (in $000, rounded to the nearest thousand):
Assuming that the population distributions are approximately normal, can we conclude at the 0.05 significance level that the difference between the two population means is greater than $60,000?
What is the decision at the 5% level of significance?

A) Fail to reject the null hypothesis and conclude that the average house prices in East Vancouver are not more than $60,000 greater than those in Oshawa.
B) Reject the null hypothesis and conclude that the average house prices in East Vancouver are not more than $60,000 greater than those in Oshawa.
C) Reject the null hypothesis and conclude that the average house prices in East Vancouver are indeed at least $60,000 greater than those in Oshawa.
D) Fail to reject the null hypothesis and conclude that the average house prices in East Vancouver are more than $60,000 greater than those in Oshawa.

Question 74

The employees at the East Vancouver office of a multinational company are demanding higher salaries than those offered at the company office located in Oshawa Ontario. Their justification for the pay difference is that the difference between the average price of single-family houses in East Vancouver and that in Oshawa is more than $60,000. Before making a decision, the company management wants to study the difference in the prices of single-family houses for sale at the two locations. The results of their search of recent house sales are as follows (in $1000, rounded to the nearest thousand):
Assuming that the population distributions are approximately normal, can we conclude at the 0.05 significance level that the difference between the two population means is greater than $60,000?
What is the value of calculated t?

A) +1.93
B) +3.22
C) -2.76
D) -2.028

Question 75

The results of a mathematics placement exam at Mercy College for two campuses is as follows: We want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2.
Using the printout above, what decision(s) can be made?

A) Looking at the P-value we conclude that there is no significant difference in the results from each campus.
B) At a 5% level of significance we conclude that there is no significant difference in the results from each campus.
C) At a 1% level of significance we conclude that campus 1 results are higher than campus 2 results.
D) Looking at the P-value we conclude that there is no significant difference in the results from each campus; we get the same conclusion when tested at a 5% level of significance.
E) Looking at the P-value we conclude that there is no significant difference in the results from each campus; however, at a 1% level of significance we conclude that campus 1 results are higher than campus 2 results.

Question 76

The employees at the East Vancouver office of a multinational company are demanding higher salaries than those offered at the company office located in Oshawa Ontario. Their justification for the pay difference is that the difference between the average price of single-family houses in East Vancouver and that in Oshawa is more than $60,000. Before making a decision, the company management wants to study the difference in the prices of single-family houses for sale at the two locations. The results of their search of recent house sales are as follows (in $1000, rounded to the nearest thousand):

Assuming that the population distributions are approximately normal, can we conclude at the 0.05 significance level that the difference between the two population means is greater than $60,000?
What is the alternate hypothesis?

A) µ₁= µ_2, or µ_d= 0
B) µ₁ $\neq$ µ_2, or µ_d $\neq$ 0
C) µ₁ - µ₂ $\le$ 60
D) µ₁- µ₂ > 60

Question 77

A local retail business wishes to determine if there is a difference in preferred indoor temperature between men and women. A random sample of data is collected, with the following results: If you were to use Excel's Data Analysis to assist in your solution to this problem, which test would you use?

A) T-test: paired 2-sample for means.
B) T-test: 2-sample assuming equal variances.
C) T-test: 2-sample assuming unequal variances.
D) Z-test: 2-sample for mean.
E) F-test: 2-sample for variances.

Question 78

The employees at the East Vancouver office of a multinational company are demanding higher salaries than those offered at the company office located in Oshawa Ontario. Their justification for the pay difference is that the difference between the average price of single-family houses in East Vancouver and that in Oshawa is more than $60,000. Before making a decision, the company management wants to study the difference in the prices of single-family houses for sale at the two locations. The results of their search of recent house sales are as follows (in $1000, rounded to the nearest thousand):

Assuming that the population distributions are approximately normal, can we conclude at the 0.05 significance level that the difference between the two population means is greater than $60,000?
If you use the 5% level of significance, what is the critical t value?

A) 2.228
B) 1.714
C) 1.833
D) $\pm$ 2.262

Question 79

The employees at the East Vancouver office of a multinational company are demanding higher salaries than those offered at the company office located in Oshawa Ontario. Their justification for the pay difference is that the difference between the average price of single-family houses in East Vancouver and that in Oshawa is more than $60,000. Before making a decision, the company management wants to study the difference in the prices of single-family houses for sale at the two locations. The results of their search of recent house sales are as follows (in $1000, rounded to the nearest thousand):

Assuming that the population distributions are approximately normal, can we conclude at the 0.05 significance level that the difference between the two population means is greater than $60,000?
If we let East Vancouver be population 1 and Oshawa be population 2, what is the null hypothesis?

A) µ₁ = µ_2, or µ_d = 0
B) µ₁ $\neq$ µ_2, or µ_d $\neq$ 0
C) µ₁ - µ₂ $\le$ 60
D) µ₁ - µ₂ > 60

Question 80

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $1000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? This example is what type of test?

A) One sample test of means.
B) Two sample test of means.
C) Paired t-test.
D) Test of proportions.