# Quiz 13: Inference About Comparing Two Populations

Statistics

Q 1Q 1

Independent samples are those for which the selection process for one is not related to the selection process for the other.

Free

True False

True

Q 2Q 2

In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference is normal if the sample sizes are both greater than 30.

Free

True False

False

Free

True False

False

Q 4Q 4

In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference if the populations are normal with equal variances.

Free

True False

Q 5Q 5

A political analyst in Iowa surveys a random sample of registered Republicans and compares the results with those obtained from a random sample of registered Democrats .This would be an example of two independent samples.

Free

True False

Q 6Q 6

Two samples of sizes 25 and 20 are independently drawn from two normal populations, where the unknown population variances are assumed to be equal.The number of degrees of freedom of the equal-variances t-test statistic is 44.

Free

True False

Q 7Q 7

The sampling distribution of is normal if the sampled populations are normal, and approximately normal if the populations are nonnormal and the sample sizes n

_{1}and n_{2}are large.Free

True False

Q 8Q 8

When the population variances are unequal, we estimate each population variance with its sample variance.Hence, the unequal-variances test statistic of is approximately Student t-distributed with n

_{1}+ n_{2} 2 degrees of freedom.Free

True False

Q 9Q 9

Unless we can conclude that the population variances are equal, we cannot use the pooled variance estimate.

Free

True False

Q 10Q 10

The equal-variances test statistic of is Student t-distributed with n

_{1}+ n_{2}degrees of freedom, provided that the two populations are normal.Free

True False

Q 11Q 11

Both the equal-variances and unequal variances test statistic and confidence interval estimator of require that the two populations be normally distributed.

Free

True False

Q 12Q 12

When the sample sizes are equal, the pooled variance of the two samples is the weighted average of the two sample variances.

Free

True False

Free

True False

Q 14Q 14

The best estimator of the difference between two population means is the difference between two sample means .

Free

True False

Q 15Q 15

When we test for differences between the means of two independent populations, we can only use a two-tailed test.

Free

True False

Free

True False

Q 17Q 17

The expected value of the difference of two sample means equals the difference of the corresponding population means when:
A) the populations are normally distributed.
B) the samples are independent.
C) the populations are approximately normal and the sample sizes are large.
D) All of these choices are true.

Free

Multiple Choice

Q 18Q 18

In testing the difference between the means of two normally distributed populations, the number of degrees of freedom associated with the unequal-variances t-test statistic usually results in a non-integer number.It is recommended that you:
A) round to the nearest integer.
B) change the sample sizes until the number of degrees of freedom becomes an integer.
C) assume that the population variances are equal, and then use df = n

_{1}+ n_{2} 2. D) None of these choices.Free

Multiple Choice

Q 19Q 19

The quantity is called the pooled variance estimate of the common variance of two unknown but equal population variances.It is the weighted average of the two sample variances, where the weights represent the:
A) sample variances.
B) sample standard deviations.
C) degrees of freedom for each sample.
D) None of these choices.

Free

Multiple Choice

Q 20Q 20

Two independent samples of sizes 20 and 30 are randomly selected from two normally distributed populations.Assume that the population variances are unknown but equal.In order to test the difference between the population means, , the sampling distribution of the sample mean difference, , is:
A) normal.
B) Student-t with 50 degrees of freedom.
C) Student-t with 48 degrees of freedom.
D) None of these choices.

Free

Multiple Choice

Q 21Q 21

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means .Assume the population variances are known.The sampling distribution of the sample mean difference is:
A) normally distributed.
B) approximately normal.
C) Student t-distributed with 88 degrees of freedom.
D) None of these choices.

Free

Multiple Choice

Q 22Q 22

Two independent samples of sizes 25 and 35 are randomly selected from two normal populations with equal variances (assumed to be unknown).In order to test the difference between the population means, the test statistic is:
A) a standard normal random variable.
B) approximately standard normal random variable.
C) Student t-distributed with 58 degrees of freedom.
D) Student t-distributed with 33 degrees of freedom.

Free

Multiple Choice

Q 23Q 23

In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference if:
A) the sample sizes are both large.
B) the populations are normal with equal variances.
C) the populations are non-normal with unequal variances.
D) All of these choices are true.

Free

Multiple Choice

Q 24Q 24

In testing the difference between two population means for which the population variances are unknown and not assumed to be equal, two independent samples are drawn from the populations.Which of the following tests is appropriate?
A) z-test
B) pooled-variances t-test
C) unequal variances t-test
D) None of these choices.

Free

Multiple Choice

Q 25Q 25

In testing the difference between the means of two normal populations using two independent samples when the population variances are unequal, the sampling distribution of the resulting statistic is:
A) normal.
B) Student-t.
C) approximately normal.
D) approximately Student-t.

Free

Multiple Choice

Q 26Q 26

In constructing a confidence interval estimate for the difference between the means of two independent normally distributed populations, we:
A) pool the sample variances when the unknown population variances are equal.
B) pool the sample variances when the population variances are known and equal.
C) pool the sample variances when the population means are equal.
D) never pool the sample variances.

Free

Multiple Choice

Q 27Q 27

The t-test for the difference between the means of two independent populations assumes that the respective:
A) sample sizes are equal.
B) populations are normal.
C) means are equal.
D) All of these choices are true.

Free

Multiple Choice

Q 28Q 28

If we are testing for the difference between the means of two independent populations with equal variances, samples of n

_{1}= 15 and n_{2}= 15 are taken, then the number of degrees of freedom is equal to A) 13 B) 14 C) 28 D) 29Free

Multiple Choice

Q 29Q 29

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom is:
A) n

_{1}+ n_{2}B) n_{1}+ n_{2} 2 C) n_{1}+ n_{2} 1 D) None of these choicesFree

Multiple Choice

Q 30Q 30

Given the information: the number of degrees of freedom that should be used in the pooled variance t-test is:
A) 40
B) 38
C) 15
D) 25

Free

Multiple Choice

Q 31Q 31

When testing vs. , the observed value of the z-score was found to be 2.15.Then, the p-value for this test would be
A) .0158
B) .0316
C) .9842
D) .9684

Free

Multiple Choice

Q 32Q 32

A political analyst in Hawaii surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of:
A) independent samples.
B) dependent samples.
C) independent samples only if the sample sizes are equal.
D) dependent samples only if the sample sizes are equal.

Free

Multiple Choice

Q 33Q 33

In testing for differences between the means of two independent populations the null hypothesis is:
A)
B)
C)
D)

Free

Multiple Choice

Q 34Q 34

Suppose we randomly selected 250 people, and on the basis of their responses to a survey we assigned them to one of two groups: high-risk group and low-risk group.We then recorded the blood pressure for the members of each group.Such data are called:
A) observational.
B) experimental.
C) matched.
D) None of these choices.

Free

Multiple Choice

Q 35Q 35

When the sample sizes are equal, the pooled variance of the two samples is the ____________________ of the two sample variances.

Free

Essay

Q 36Q 36

The equal-variances test statistic of is Student t-distributed with n

_{1}+ n_{2} 2 degrees of freedom provided that the two populations are ____________________.Free

Essay

Q 37Q 37

The unequal-variances test statistic of has an approximate ____________________ distribution with degrees of freedom.

Free

Essay

Q 38Q 38

____________________ samples are those for which the selection process for one is not related to the selection process for the other.

Free

Essay

Q 39Q 39

When two population variances are ____________________ we estimate each population variance with its sample variance.The test statistic of is approximately Student t-distributed with n

_{1}+ n_{2} 2 degrees of freedom.Free

Essay

Q 40Q 40

A political analyst in Iowa surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of ____________________ samples.

Free

Essay

Q 41Q 41

The pooled-variances t-test is used when the two population variances are ____________________.

Free

Essay

Q 42Q 42

When the population variances are unknown and unequal, we estimate each population variance with its ____________________ variance.

Free

Essay

Q 43Q 43

The pooled variance estimator is the ____________________ average of the two sample variances.

Free

Essay

Q 44Q 44

Aptitude Test Scores
Two random samples of 40 students were drawn independently from two populations of students.Assume their aptitude tests are normally distributed (total points = 100).The following statistics regarding their scores in an aptitude test were obtained: .
-{Aptitude Test Scores Narrative} Test at the 5% significance level to determine whether we can infer that the two population means differ.

Free

Essay

Q 45Q 45

Aptitude Test Scores
Two random samples of 40 students were drawn independently from two populations of students.Assume their aptitude tests are normally distributed (total points = 100).The following statistics regarding their scores in an aptitude test were obtained: .
-{Aptitude Test Scores Narrative} Estimate with 95% confidence the difference between the two population means.

Free

Essay

Q 46Q 46

Aptitude Test Scores
Two random samples of 40 students were drawn independently from two populations of students.Assume their aptitude tests are normally distributed (total points = 100).The following statistics regarding their scores in an aptitude test were obtained: .
-{Aptitude Test Scores Narrative} Explain how to use the 95% confidence interval to test the hypotheses at = .05.

Free

Essay

Q 47Q 47

Starting Salary
In testing the hypotheses vs. , two random samples from two populations of college of business graduates majoring in global marketing and international business produced the following statistics regarding their starting salaries (in $1000s): , , , , , and .(Assume the salaries have normal distributions.)
-{Starting Salary Narrative} What conclusion can we draw at the 5% significance level?

Free

Essay

Q 48Q 48

Starting Salary
In testing the hypotheses vs. , two random samples from two populations of college of business graduates majoring in global marketing and international business produced the following statistics regarding their starting salaries (in $1000s): , , , , , and .(Assume the salaries have normal distributions.)
-{Starting Salary Narrative} Estimate with 95% confidence the difference between the two population means.

Free

Essay

Q 49Q 49

Starting Salary
In testing the hypotheses vs. , two random samples from two populations of college of business graduates majoring in global marketing and international business produced the following statistics regarding their starting salaries (in $1000s): , , , , , and .(Assume the salaries have normal distributions.)
-{Starting Salary Narrative} Explain how to use the 95% confidence interval to test the hypotheses at = .05.

Free

Essay

Q 50Q 50

The service manager of a car dealer wants to determine if owners of new cars (two years old or less) tune up their cars more frequently than owners of older cars (more than two years old).From his records he takes a random sample of ten new cars and ten older cars and determines the number of times the cars were tuned up in the last 12 months.The data follow.Do these data allow the service station owner to infer at the 10% significance level that new car owners tune up their cars more frequently than older car owners?

Free

Essay

Q 51Q 51

Undergraduates' Test Scores
35 undergraduate students who completed two years of college were asked to take a basic mathematics test.The mean and standard deviation of their scores were 75.1 and 12.8, respectively.In a random sample of 50 students who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively.
-{Undergraduates' Test Scores Narrative} Can we infer at the 10% significance level that a difference exists between the two groups?

Free

Essay

Q 52Q 52

Undergraduates' Test Scores
35 undergraduate students who completed two years of college were asked to take a basic mathematics test.The mean and standard deviation of their scores were 75.1 and 12.8, respectively.In a random sample of 50 students who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively.
-{Undergraduates' Test Scores Narrative} Estimate with 90% confidence the difference in mean scores between the two groups of students.

Free

Essay

Q 53Q 53

Undergraduates' Test Scores
35 undergraduate students who completed two years of college were asked to take a basic mathematics test.The mean and standard deviation of their scores were 75.1 and 12.8, respectively.In a random sample of 50 students who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively.
-{Undergraduates' Test Scores Narrative} Explain how to use the interval estimate to test the hypotheses.

Free

Essay

Q 54Q 54

Additives
A food processor wants to compare two additives for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with additive A and 16 are treated with additive B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below
-{Additives Narrative} State the null and alternative hypotheses to determine if the average number of hours until spoilage begins differs for the additives A and B.

Free

Essay

Q 55Q 55

Additives
A food processor wants to compare two additives for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with additive A and 16 are treated with additive B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below
-{Additives Narrative} Assume population variances are equal.Calculate the pooled variance and the value of the test statistic.

Free

Essay

Q 56Q 56

Additives
A food processor wants to compare two additives for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with additive A and 16 are treated with additive B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below
-{Additives Narrative} Determine the rejection region at = .05 and write the proper conclusion.

Free

Essay

Q 57Q 57

A calculus professor wanted to test whether the grades on calculus test were the same for upper and lower classmen.The professor took a random sample of size 12 from each group.For this situation, the professor should use a matched pairs t-test.

Free

True False

Q 58Q 58

Two measurements from the same individuals is an example of data collected from a matched pairs experiment.

Free

True False

Free

True False

Q 60Q 60

In comparing the difference in means with a matched pairs experiment, the variable under consideration is , where the subscript D refers to the difference.

Free

True False

Q 61Q 61

The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 8 pairs, is 7.

Free

True False

Q 62Q 62

When comparing two population means using data that are gathered from a matched pairs experiment, the test statistic for

_{D}is Student t-distributed with v = n_{D} 1 degrees of freedom, provided that the differences are normally distributed.Free

True False

Q 63Q 63

In comparing two population means of interval data, we must decide whether the samples are independent (in which case the parameter of interest is ) or matched pairs (in which case the parameter is

_{D}) in order to select the correct test statistic.Free

True False

Q 64Q 64

If there are 10 pairs of data in a matched pairs experiment, the degrees of freedom for the corresponding t-test is 18.

Free

True False

Q 65Q 65

A Marine boot camp instructor recorded the time in which each of 15 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred, the instructor would use a t-distribution with 15 degrees of freedom.

Free

True False

Q 66Q 66

A test is being conducted to test the difference between two population means using data that are gathered from a matched pairs experiment.If the paired differences are normal, then the distribution used for testing is the:
A) normal distribution.
B) binomial distribution.
C) Student t-distribution.
D) F-distribution.

Free

Multiple Choice

Q 67Q 67

If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2, the second observation of sample 1 with the second observation of sample 2, and so on, the samples are referred to as:
A) matched pairs.
B) independent samples.
C) nonrandom samples.
D) None of these choices.

Free

Multiple Choice

Q 68Q 68

The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 10 pairs, is:
A) 10
B) 20
C) 9
D) 18

Free

Multiple Choice

Q 69Q 69

The symbol refers to:
A) the difference in the means of two independent populations.
B) one matched pairs difference.
C) the mean difference in the pairs of observations.
D) None of these choices.

Free

Multiple Choice

Free

Multiple Choice

Q 71Q 71

Two measurements from the same individuals is an example of data collected from a(n) ____________________ experiment.

Free

Essay

Q 72Q 72

The test for the mean difference in a matched pairs design requires the differences to have a(n) ____________________ distribution.

Free

Essay

Q 73Q 73

The degrees of freedom for a test of the mean of the paired differences is the number of ____________________ minus ____________________.

Free

Essay

Q 74Q 74

In a matched pairs experiment the parameter of interest is the ____________________ of the population of ____________________.

Free

Essay

Q 75Q 75

If you are testing to see if a weight loss program is working, and you subtract the weights before after for a group of 10 people, the alternative hypothesis is that the mean difference is ____________________ 0.

Free

Essay

Q 76Q 76

If you are testing to see if a weight loss program is working, and you subtract the weights after before for a group of 10 people, the alternative hypothesis is that the mean difference is ____________________ 0.

Free

Essay

Q 77Q 77

In testing the hypothesis vs. , two random samples from two normal populations produced the following statistics: .What conclusion can we draw at the 1% significance level?

Free

Essay

Q 78Q 78

Engine Wear
To compare the wearing of two types of automobile engines, 1 and 2, an experimenter chose to "pair" the measurements, comparing the wear for the two types of engines on each of 7 automobiles, as shown below.
-(Engine Wear Narrative} Determine whether these data are sufficient to infer at the 10% significance level that the two types of engines wear differently.

Free

Essay

Q 79Q 79

Engine Wear
To compare the wearing of two types of automobile engines, 1 and 2, an experimenter chose to "pair" the measurements, comparing the wear for the two types of engines on each of 7 automobiles, as shown below.
-{Engine Wear Narrative} Estimate with 90% confidence the mean difference and interpret.

Free

Essay

Q 80Q 80

Promotional Campaigns
The general manager of a chain of fast food chicken restaurants wants to determine how effective their promotional campaigns are.In these campaigns "20% off" coupons are widely distributed.These coupons are only valid for one week.To examine their effectiveness, the executive records the daily gross sales (in $1,000s) in one restaurant during the campaign and during the week after the campaign ends.The data is shown below.
-{Promotional Campaigns Narrative} Can they infer at the 5% significance level that sales increase during the campaign?

Free

Essay

Q 81Q 81

Promotional Campaigns
The general manager of a chain of fast food chicken restaurants wants to determine how effective their promotional campaigns are.In these campaigns "20% off" coupons are widely distributed.These coupons are only valid for one week.To examine their effectiveness, the executive records the daily gross sales (in $1,000s) in one restaurant during the campaign and during the week after the campaign ends.The data is shown below.
-{Promotional Campaigns Narrative} Estimate with 95% confidence the mean difference and interpret.

Free

Essay

Q 82Q 82

Motorcycle insurance appraisers examine motorcycles that have been involved in accidental collisions to assess the cost of repairs.An insurance executive is concerned that different appraisers produce significantly different assessments.In an experiment 10 motorcycles that have recently been involved in accidents were shown to two appraisers.Each assessed the estimated repair costs.These results are shown below.Can the executive conclude at the 5% significance level that the appraisers differ in their assessments?

Free

Essay

Q 83Q 83

Clothing Expenditures
A marketing consultant was in the process of studying the perceptions of married couples concerning their monthly clothing expenditures.He believed that the husband's perception would be higher than the wife's.To judge his belief, he takes a random sample of ten married couples and asks each spouse to estimate the family clothing expenditure (in dollars) during the previous month.The data are shown below.
-{Clothing Expenditures Narrative} Can the consultant conclude at the 5% significance level that the husband's estimate is higher than the wife's estimate?

Free

Essay

Q 84Q 84

Clothing Expenditures
A marketing consultant was in the process of studying the perceptions of married couples concerning their monthly clothing expenditures.He believed that the husband's perception would be higher than the wife's.To judge his belief, he takes a random sample of ten married couples and asks each spouse to estimate the family clothing expenditure (in dollars) during the previous month.The data are shown below.
-{Clothing Expenditures Narrative} Estimate with 95% confidence the population mean difference.

Free

Essay

Q 85Q 85

Clothing Expenditures
A marketing consultant was in the process of studying the perceptions of married couples concerning their monthly clothing expenditures.He believed that the husband's perception would be higher than the wife's.To judge his belief, he takes a random sample of ten married couples and asks each spouse to estimate the family clothing expenditure (in dollars) during the previous month.The data are shown below.
-{Clothing Expenditures Narrative} Briefly describe what the interval estimate tells you.

Free

Essay

Q 86Q 86

A behaviorist has performed the following experiment.For each of 10 sets of identical twins who were born 30 years ago, he recorded their annual incomes, according to which twin was born first.The results (in $1,000s) are shown below.Can he infer at 5% significance level that there is a difference in income between the twins?

Free

Essay

Free

True False

Free

True False

Q 89Q 89

In testing for the equality of two population variances, when the populations are normally distributed, the 5% level of significance has been used.To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of .05.

Free

True False

Q 90Q 90

When testing the equality of two population variances the number in the null hypothesis is 0.

Free

True False

Q 91Q 91

When the necessary conditions are met, a two-tail test is being conducted at = .05 to test .The two sample variances are and , and the sample sizes are n

_{1}= 25 and n_{2}= 25.The calculated value of the test statistic will be F = 2.Free

True False

Q 92Q 92

The F-test used for testing the difference in 2 population variances is always a one-tailed test.

Free

True False

Q 93Q 93

The test for the equality of two population variances assumes that each of the two populations is normally distributed.

Free

True False

Free

True False

Free

True False

Free

True False

Q 97Q 97

The test statistic employed to test is is F-distributed with v

_{1}= n_{1} 1 and v_{2}= n_{2} 1 degrees of freedom if the two populations are F-distributed.Free

True False

Q 98Q 98

The F-distribution is the sampling distribution of the ratio of:
A) two sample variances.
B) two normal population means.
C) two normal population variances.
D) None of these choices.

Free

Multiple Choice

Q 99Q 99

Which of the following statements is false for an F-distribution?
A) Variables that are F-distributed range from 0 to .
B) The exact shape of the distribution is determined by two numbers of degrees of freedom.
C) The degrees of freedom for the numerator can be larger than, smaller than, or equal to the degrees of freedom for the denominator.
D) All of these choices are true.

Free

Multiple Choice

Q 100Q 100

When testing for the difference between two population variances with sample sizes of n

_{1}= 8 and n_{2}= 10, the degrees of freedom are: A) 8 and 10 B) 7 and 9 C) 2 and 18 D) 18 and 2Free

Multiple Choice

Q 101Q 101

Which of the following statements is correct regarding the percentile points of the F-distribution?
A) F

_{.05,10,20}= 1/F_{.95,10,20}B) F_{.05,10,20}= 1/F_{.05,20,10}C) F_{.95,10,20}= 1/F_{.05,20,10}D) F_{.95,10,20}= 1/F_{.95,20,10}Free

Multiple Choice

Q 102Q 102

The ratio of two independent chi-squared variables divided by their degrees of freedom is:
A) normally distributed
B) Student t-distributed
C) chi-squared distributed
D) F-distributed

Free

Multiple Choice

Q 103Q 103

In testing for the equality of two population variances, when the populations are normally distributed, the 10% level of significance has been used.To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of:
A) .90
B) .20
C) .10
D) .05

Free

Multiple Choice

Q 104Q 104

The statistical distribution used for testing the difference between two population variances is the
A) Student t-distribution
B) standard normal distribution
C) F-distribution
D) None of these choices.

Free

Multiple Choice

Q 105Q 105

The test for the equality of two population variances is based on the:
A) difference between the two sample variances.
B) ratio of the two sample variances.
C) sum of the two sample variances.
D) product of the two sample variances.

Free

Multiple Choice

Q 106Q 106

Two independent samples are drawn from two normal populations, where the population variances are assumed to be equal.The sampling distribution of the ratio of the two sample variances is:
A) normal
B) Student-t
C) F
D) chi-squared

Free

Multiple Choice

Q 107Q 107

The sampling distribution of the ratio of two sample variances is said to be F-distributed provided that:
A) the samples are independent from any distributions.
B) the populations are normal with equal variances.
C) the samples are matched and their sizes are large.
D) the samples are independently drawn from two normal populations.

Free

Multiple Choice

Q 108Q 108

To estimate the ratio of the population variances you use the ____________________ of the ____________________ variances.

Free

Essay

Q 109Q 109

The sampling distribution of the ratio of two (independent) sample variances is said to be ____________________ distributed.

Free

Essay

Q 110Q 110

The sampling distribution of the ratio of two sample variances is said to be F-distributed provided that we have two ____________________ samples drawn from their respective populations.

Free

Essay

Q 111Q 111

The test statistic for testing for the equality of two population variances has a(n) ____________________ distribution.

Free

Essay

Q 112Q 112

The test statistic for testing for the equality of two population variances has an F-distribution with ____________________ and ____________________ degrees of freedom.

Free

Essay

Q 113Q 113

If the F-test statistic is large, that means the variance of Population 1 is ____________________ than/to the variance of Population 2.

Free

Essay

Q 114Q 114

When testing for the equality of two population variances the number in the null hypothesis is ____________________.

Free

Essay

Free

Essay

Q 116Q 116

Random samples from two normal populations produced the following statistics: , , , and .Is there enough evidence at the 5% significance level to infer that the variance of Population 1 is larger than the variance of Population 2?

Free

Essay

Q 117Q 117

Fitness Program
A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program.However, he will not perform the equal-variance t-test of the difference between the population means if the condition necessary for its use is not satisfied.The number of pound lost at the of the program data follow:
-{Fitness Program Narrative} Can the statistician conclude at the 5% significance level that the required condition is not satisfied?

Free

Essay

Q 118Q 118

Fitness Program
A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a fitness program.However, he will not perform the equal-variance t-test of the difference between the population means if the condition necessary for its use is not satisfied.The number of pound lost at the of the program data follow:
-{Fitness Program Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.

Free

Essay

Q 119Q 119

Profit Margin
An investor is considering two types of investment.She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2.However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2.To help make her decision, she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2.She finds that the sample variances of Investments 1 and 2 are 225 and 118, respectively.
-{Profit Margin Narrative} Can she infer at the 5% significance level that the population variance of investment 1 exceeds that of investment 2?

Free

Essay

Q 120Q 120

Profit Margin
An investor is considering two types of investment.She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2.However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2.To help make her decision, she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2.She finds that the sample variances of Investments 1 and 2 are 225 and 118, respectively.
-{Profit Margin Narrative} Estimate with 95% confidence the ratio of the two population variances.

Free

Essay

Q 121Q 121

Profit Margin
An investor is considering two types of investment.She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2.However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2.To help make her decision, she randomly selects seven monthly profit margins on investment 1 and ten monthly profit margins on investment 2.She finds that the sample variances of Investments 1 and 2 are 225 and 118, respectively.
-{Profit Margin Narrative} Briefly describe what the interval estimate tells you.

Free

Essay

Q 122Q 122

Clinic Waiting Time
In a random sample of 20 patients who visited a clinic at Medical Center 1, a researcher found that the variance of the waiting time (in minutes) was 128.0.In a random sample of 15 patients in the clinic of Medical Center 2, the researcher found the variance to be 178.8.
-{Clinic Waiting Time Narrative} Can we infer at the 5% level of significance that the population variances differ?

Free

Essay

Q 123Q 123

Clinic Waiting Time
In a random sample of 20 patients who visited a clinic at Medical Center 1, a researcher found that the variance of the waiting time (in minutes) was 128.0.In a random sample of 15 patients in the clinic of Medical Center 2, the researcher found the variance to be 178.8.
-{Clinic Waiting Time Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.

Free

Essay

Q 124Q 124

Antioxidants
A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below
-{Antioxidants Narrative} State the null and alternative hypotheses for determining if the population variances differ for Antioxidants A and B.

Free

Essay

Q 125Q 125

Antioxidants
A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below
-{Antioxidants Narrative} Determine the rejection region for testing the equality of the two population variances at = .05.

Free

Essay

Q 126Q 126

Antioxidants
A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below
-{Antioxidants Narrative} Calculate the value of the test statistic for testing the equality of the population variances, and write the proper conclusion.

Free

Essay

Q 127Q 127

Antioxidants
A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below
-{Antioxidants Narrative} Develop the 95% confidence interval estimate of the ratio of the two population variances.

Free

Essay

Q 128Q 128

Antioxidants
A food processor wants to compare two antioxidants for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with antioxidant A and 16 are treated with antioxidant B, and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below
-{Antioxidants Narrative} Explain how to use the 95% confidence interval for testing the equality of the two population variances at the 5% level.

Free

Essay

Q 129Q 129

The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by some non-zero number.

Free

True False

Q 130Q 130

In constructing a confidence interval estimate for the difference between two population proportions, we pool the population proportions when the populations are normally distributed.

Free

True False

Q 131Q 131

The pooled proportion estimate is found by taking the proportion of successes from sample 1 plus the proportion of successes from sample 2.

Free

True False

Free

True False

Q 133Q 133

A required condition for using the normal approximation to the binomial in testing the difference between two population proportions is that n

_{1}p_{1} 30 and n_{2}p_{2} 30.Free

True False

Free

True False

Q 135Q 135

The pooled proportion estimate is used when the proportion of successes from sample 1 equals the proportion of successes from sample 2.

Free

True False

Q 136Q 136

The difference in two sample proportions is an unbiased consistent estimator of the difference in their respective population proportions.

Free

True False

Q 137Q 137

The expected value of the difference between two sample proportions is the difference between their corresponding population proportions.

Free

True False

Q 138Q 138

The variance of the difference in sample proportions equals the difference of their population variances.

Free

True False

Q 139Q 139

For testing the difference between two population proportions, the pooled proportion estimate should be used to compute the value of the test statistic when the:
A) populations are normally distributed.
B) sample sizes are small.
C) null hypothesis states that the two population proportions are equal.
D) samples are independently drawn from the populations.

Free

Multiple Choice

Q 140Q 140

The pooled proportion estimate is used when:
A) the proportion of successes from sample 1 equals the proportion of successes from sample 2.
B) the total number of successes in both samples divided by the total of both sample sizes equals 1.
C) the null hypothesis states that the two population proportions differ by some non-zero number.
D) None of these choices.

Free

Multiple Choice

Q 141Q 141

For testing the difference between two population proportions, the pooled proportion estimate is found by taking:
A) the proportion of successes from sample 1 plus the proportion of successes from sample 2.
B) the total number of successes in both samples divided by the total of both sample sizes.
C) the difference between the proportion of successes in each sample.
D) None of these choices.

Free

Multiple Choice

Q 142Q 142

In constructing a confidence interval estimate for the difference between two population proportions, we:
A) pool the population proportions when the populations are normally distributed.
B) pool the population proportions when the population means are equal.
C) pool the population proportions when they are equal.
D) never pool the population proportions.

Free

Multiple Choice

Q 143Q 143

Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?
A)
B) ,,, and
C) ,,, and
D) Choice b is the true requirement, but choice c is the one you actually check.

Free

Multiple Choice

Q 144Q 144

The difference in two sample proportions is a(n) ____________________ estimator of the difference in their respective population proportions.

Free

Essay

Q 145Q 145

Pooling is made possible by hypothesizing (under the null hypothesis) that p

_{1}__________ p_{2}.Free

Essay

Q 146Q 146

The pooled proportion estimate is used when the null hypothesis states that the two population proportions differ by ____________________.

Free

Essay

Q 147Q 147

In constructing a confidence interval estimate for the difference between two population proportions, we ____________________ (always/sometimes/never) pool the population proportions.

Free

Essay

Q 148Q 148

The variance of the difference between two sample proportions equals the ____________________ of their population proportion variances.

Free

Essay

Q 149Q 149

The expected value of the difference between two sample proportions is the ____________________ of/between their corresponding population proportions.

Free

Essay

Q 150Q 150

If the sample sizes are large enough so the conditions are met, the difference between two sample proportions has an approximate ____________________ distribution.

Free

Essay

Q 151Q 151

When the data from two populations are ____________________ the parameter to be tested and estimated is the difference between the two population proportions.

Free

Essay

Q 152Q 152

Headache Medicine
A researcher wants to see if/how men and women differ in their reaction to a headache medicine with respect to drowsiness.In testing the hypotheses vs. , the following statistics were obtained: n

_{1}= 400, x_{1}= 208, n_{2}= 250, and x_{2}= 115, where x_{1}and x_{2}represent the number of patients in the two samples (men vs.women) who reported to have drowsiness as a result of taking headache medicine. -{Headache Medicine Narrative} What conclusion can we draw at the 10% significance level?Free

Essay

Q 153Q 153

Headache Medicine
A researcher wants to see if/how men and women differ in their reaction to a headache medicine with respect to drowsiness.In testing the hypotheses vs. , the following statistics were obtained: n

_{1}= 400, x_{1}= 208, n_{2}= 250, and x_{2}= 115, where x_{1}and x_{2}represent the number of patients in the two samples (men vs.women) who reported to have drowsiness as a result of taking headache medicine. -{Headache Medicine Narrative} Estimate with 90% confidence the difference between the two population proportions.Free

Essay

Q 154Q 154

TV Sex
A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television.In a survey of 1,500 Americans, 810 believe that there is too much television sex.
-{TV Sex Narrative} Can we infer at the 99% significance level that the proportion of Canadians and Americans who believe that there is too much sex on television differ?

Free

Essay

Q 155Q 155

TV Sex
A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television.In a survey of 1,500 Americans, 810 believe that there is too much television sex.
-{TV Sex Narrative} Estimate with 99% confidence the difference in the proportion of Canadians and Americans who believe that there is too much sex on television.

Free

Essay

Q 156Q 156

TV Sex
A survey of 1,500 Canadians reveals that 945 believe that there is too much sex on television.In a survey of 1,500 Americans, 810 believe that there is too much television sex.
-{TV Sex Narrative} Briefly explain what the interval estimate tells you.

Free

Essay

Q 157Q 157

A councilwoman regularly polls her constituency to gauge her level of support among voters.This month, 652 out of 1158 voters support her.Five months ago, 412 out of 982 voters supported her.With a 5% significance level, can she infer that support has increased by at least 10 percentage points?

Free

Essay

Q 158Q 158

Senatorial Election
A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate.
-{Senatorial Election Narrative} Can we infer at the 5% significance level that the proportions of male and female voters who intend to vote for the Democrat candidate differ?

Free

Essay

Q 159Q 159

Senatorial Election
A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate.
-{Senatorial Election Narrative} What is the p-value of the test?

Free

Essay

Q 160Q 160

Senatorial Election
A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate.
-{Senatorial Election Narrative} Estimate with 95% confidence the difference in the proportion of male and female voters who intend to vote for the Democrat candidate.

Free

Essay

Q 161Q 161

Senatorial Election
A political poll immediately prior to a senatorial election reveals that 145 out of 250 male voters and 105 out of 200 female voters intend to vote for the Democrat candidate.
-{Senatorial Election Narrative} Explain how to use the interval estimate to test the hypotheses.

Free

Essay

Q 162Q 162

Mass Production Line
A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines.The completed sheet is shown below.
-{Mass Production Line Narrative} Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2?

Free

Essay

Q 163Q 163

Mass Production Line
A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines.The completed sheet is shown below.
-{Mass Production Line Narrative} What is the p-value of the test? Explain how to use it for testing the hypotheses.

Free

Essay

Q 164Q 164

Mass Production Line
A quality control examiner keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines.The completed sheet is shown below.
-{Mass Production Line Narrative} Estimate with 95% confidence the difference in population proportions.

Free

Essay

Q 165Q 165

Worker Safety
An OSHA agent wanted to determine if efforts to promote safety have been successful.By checking the records of 250 workers, he found that 30 of them suffered either minor or major injuries that year.A random sample of 400 workers last year revealed that 80 suffered some form of injury.
-{Worker Safety Narrative} Can the statistician infer at the 5% significance level that efforts to promote safety have been successful?

Free

Essay

Q 166Q 166

Worker Safety
An OSHA agent wanted to determine if efforts to promote safety have been successful.By checking the records of 250 workers, he found that 30 of them suffered either minor or major injuries that year.A random sample of 400 workers last year revealed that 80 suffered some form of injury.
-{Worker Safety Narrative} What is the p-value of the test? Explain how to use it for testing the hypotheses.

Free

Essay

Q 167Q 167

Worker Safety
An OSHA agent wanted to determine if efforts to promote safety have been successful.By checking the records of 250 workers, he found that 30 of them suffered either minor or major injuries that year.A random sample of 400 workers last year revealed that 80 suffered some form of injury.
-{Worker Safety Narrative} Estimate with 95% confidence the difference in population proportions.

Free

Essay

Q 168Q 168

Speed Limits Violation
Do out-of-state motorists violate the speed limit more frequently than in-state motorists? This vital question was addressed by the highway patrol in a large eastern state.A random sample of the speeds of 2,500 randomly selected cars was categorized according to whether the car was registered in the state or in some other state and whether or not the car was violating the speed limit.The data follow.
-{Speed Limits Violation Narrative} Do these data provide enough evidence to support the highway patrol's claim at the 5% significance level?

Free

Essay

Q 169Q 169

Speed Limits Violation
Do out-of-state motorists violate the speed limit more frequently than in-state motorists? This vital question was addressed by the highway patrol in a large eastern state.A random sample of the speeds of 2,500 randomly selected cars was categorized according to whether the car was registered in the state or in some other state and whether or not the car was violating the speed limit.The data follow.
-{Speed Limits Violation Narrative} Estimate with 95% confidence the difference in population proportions.

Free

Essay

Q 170Q 170

Speed Limits Violation
Do out-of-state motorists violate the speed limit more frequently than in-state motorists? This vital question was addressed by the highway patrol in a large eastern state.A random sample of the speeds of 2,500 randomly selected cars was categorized according to whether the car was registered in the state or in some other state and whether or not the car was violating the speed limit.The data follow.
-{Speed Limits Violation Narrative} Briefly describe what the interval estimate tells you.

Free

Essay