Deck 11: Two-Sample Tests of Hypothesis

Question 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 1

False

Question 2

The paired difference test has (n - 1)degrees of freedom.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

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.

Question 6

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

Question 7

In testing the difference between two population proportions,we pool the two sample proportions to estimate the population proportion.

Question 8

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

Question 9

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.

Question 10

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.

Question 11

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

Question 12

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.

Question 13

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

Question 14

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

Question 15

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.

Question 16

When testing for a difference between the means of two dependent samples,n₁ = n₂.

Question 17

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations,the degrees of freedom are computed as (n₁)(n₂)- 1.

Question 18

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.

Question 19

A statistics professor wants to compare grades in two different classes of the same course.This is an example of a paired sample.

Question 20

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

Question 21

How is a pooled estimate of the population proportion represented?

A)p_c
B)z
C) $\pi$
D)n $\pi$

Question 22

When dependent samples are used to test for differences in the means,we compute paired differences.

Question 23

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.

Question 24

For a hypothesis test comparing two population means,the combined degrees of freedom are 24.Which of the following statements about the two sample sizes is NOT true? 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

Question 25

Suppose we test 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 26

In a market test of a new chocolate raspberry coffee,a poll of 400 people from Dobbs Ferry showed 250 preferred the new coffee.In Irvington,170 out of 350 people preferred the new coffee.To test the hypothesis that there is no difference in preferences between the two villages,what is the alternate hypothesis?

A)Option A
B)Option B
C)Option C
D)Option D

Question 27

When independent samples are used to test for differences in the means,we pool the sample variances.

Question 28

In a market test of a new chocolate raspberry coffee,a poll of 400 people (sample 1)from Dobbs Ferry showed 250 preferred the new coffee.In Irvington,170 (sample 2)out of 350 people preferred the new coffee.To test the hypothesis that a higher proportion of people in Dobbs Ferry prefer the new coffee,what is the alternate hypothesis?

A)Option A
B)Option B
C)Option C
D)Option D

Question 29

For a hypothesis comparing two population means,what is the critical value for a one-tailed hypothesis test,using a 5% level of significance level,with both sample sizes equal to 13? Assume the population standard deviations are equal.

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

Question 30

When dependent samples are used to test for differences in the means,we pool the sample variances.

Question 31

The net weights (in grams)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: 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

Question 32

If two dependent samples of size 20 are used to test the difference between the means,the degrees of freedom for a t-statistic is 19.

Question 33

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

Question 34

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

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

Question 35

If two independent samples of size 10 are used to test the difference between the means,the degrees of freedom for a t-statistic are 18.

Question 36

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

A)Option A
B)Option B
C)Option C
D)Option D

Question 37

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.

Question 38

Using two independent samples,we test for a hypothesized difference between two population means.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

Question 39

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 40

For a hypothesis comparing two population means,what is the critical value for a one-tailed hypothesis test,using a 5% level of significance level,with both sample sizes equal to 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

Question 41

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. What is the alternate hypothesis?

A)Option A
B)Option B
C)Option C
D)Option D

Question 42

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. If the calculated value of t is +2.70,what would be the decision using 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 43

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.

Question 44

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. What is the degrees of freedom?

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

Question 45

The results of a mathematics placement exam at two different campuses of Mercy College follow: Given that the two population standard deviations are known,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 46

The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the computed value of the test statistic?

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

Question 47

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 $ thousands)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)Option A
B)Option B
C)Option C
D)Option D

Question 48

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. What is the null hypothesis?

A)Option A
B)Option B
C)Option C
D)Option D

Question 49

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 $ thousands)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 50

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 $ thousands)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)+2.132
B) $\pm$ 2.776
C)+2.262
D) $\pm$ 2.228

Question 51

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. If we test the null hypothesis at the 1% level of significance,what is the decision?

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 52

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. 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 53

Two samples,one of size 14 and the second of size 13,are selected to test the difference between two 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

Question 54

Of 250 adults who tried a new multi-grain cereal,"Wow!",187 rated it excellent;of 100 children sampled,66 rated it excellent.What is the pooled proportion?

A)0.723
B)1.408
C)0.494
D)0.807

Question 55

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. What is the computed value of t?

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

Question 56

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. 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 57

The results of a mathematics placement exam at two different campuses of Mercy College follow: 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)Option A
B)Option B
C)Option C
D)Option D

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 hypothesis not equal to ,what is the null hypothesis?

A)Option A
B)Option B
C)Option C
D)Option D

Question 59

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 60

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 $ thousands)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)Option A
B)Option B
C)Option C
D)Option D

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 $ thousands)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.

Question 62

For hypotheses that compare two population means,what test statistic if used when the population standard deviations are known?

Question 63

A financial planner wants to compare the yield of income and growth mutual funds.Fifty thousand dollars is invested in each of a sample of 35 income and 40 growth funds.The mean increase for a two-year period for the income funds is $900.For the growth funds the mean increase is $875.Income funds have a population standard deviation of $35;growth funds have a population standard deviation of $45.At the 0.05 significance level,is there a difference in the mean yields of the two funds?
What decision is made about the null hypothesis using and $\alpha$ = 0.05? ____________

Question 64

What is the purpose of pooling the sample variances when testing the difference between two population means? ___________

Question 65

A study by a bank compared the average savings of customers who were depositors for three years or less,with those who had been depositors for more than three years.The results of a sample are: What is the p-value if the test statistic is 1.51? _____

Question 66

A financial planner wants to compare the yield of income and growth mutual funds.Fifty thousand dollars is invested in each of a sample of 35 income and 40 growth funds.The mean increase for a two-year period for the income funds is $900.For the growth funds the mean increase is $875.Income funds have a population standard deviation of $35;growth funds have a population standard deviation of $45.At the 0.05 significance level,is there a difference in the mean yields of the two funds?
What is the null hypothesis? __________________

Question 67

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 $ thousands)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 68

When can a paired-t test be used to test a hypothesis of no difference between population means?

Question 69

A hypothesis tests that two population means are equal.A sample of 10 with a standard deviation of 5 is selected from the first population and a sample of 15 with a standard deviation of 5 from the second population.The standard deviations are equal.Testing the claim at the 0.01 level,what is the critical value? Assume unequal standard deviations.

A)3.355
B)3.169
C)2.896
D)2.764

Question 70

What is the purpose of pooling the sample proportions when testing the difference between two population proportions? ___________

Question 71

For hypotheses that compare two population means,when is a pooled variance used?

Question 72

A study by a bank compared the average savings of customers who were depositors for three years or less,with those who had been depositors for more than three years.The results of a sample are: What is the p-value if $\alpha$ = .05 and the test statistic is 3.15? _____

Question 73

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? What is your decision? ____________________

Question 74

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? What is your decision if $\alpha$ = 0.01 and the z-statistic is -1.96? ____________________

Question 75

A study by a bank compared the average savings of customers who were depositors for three years or less,with those who had been depositors for more than three years.The results of a sample are: If $\alpha$ = .05 and the p-value is 0.146,what is the decision rule regarding the null hypothesis?

Question 76

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 $ thousands)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)+1.93
B) $\pm$ 2.776
C)+0.47
D)-2.028

Question 77

For hypotheses that compare two population means,what test statistic if used when the population standard deviations are unknown?