Deck 13: Inference About Comparing Two Populations, Part 2

Question 1

Pooling is made possible by hypothesizing (under the null hypothesis) that p₁ = p₂.

Answer 1

True

Question 2

When the necessary conditions are met, a two-tail test is being conducted at $\alpha$ = 0.05 to test . The two sample variances are and , and the sample sizes are n₁ = 25 and n₂ = 25. The calculated value of the test statistic will be F = 2.

Answer 2

False

Question 3

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

Answer 3

False

Question 4

A required condition for using the normal approximation to the binomial in testing the difference between two population proportions is that n₁p₁ $\ge$ 30 and n₂p₂ $\ge$ 30.

Question 5

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

Question 6

The F-distribution is symmetric.

Question 7

All F-tests for the equality of two population variances are one-tailed tests.

Question 8

When comparing two population variances, we use the ratio rather than the difference .

Question 9

The test statistic employed to test is is F-distributed with v₁ = n₁ - 1 and v₂ = n₂ - 1 degrees of freedom if the two populations are F-distributed.

Question 10

The F-distribution can only have non-negative values.

Question 11

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

Question 12

We use a t-test to determine whether two population variances are equal.

Question 13

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

Question 14

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

Question 15

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 0.05.

Question 16

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

Question 17

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

Question 18

In comparing two population means the statistic under consideration is .

Question 19

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

Question 20

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

Question 21

Which of the following statements is false for an F-distribution?

A) Variables that are F-distributed range from 0 to $\infty$ .
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.

Question 22

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

Question 23

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

Question 24

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.

Question 25

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.

Question 26

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

Question 27

When testing for the difference between two population variances with sample sizes of n₁ = 8 and n₂ = 10, the degrees of freedom are:

A) 8 and 10
B) 7 and 9
C) 2 and 18
D) 18 and 2

Question 28

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

Question 29

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) 0.90
B) 0.20
C) 0.10
D) 0.05

Question 30

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

Question 31

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.

Question 32

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

A) F_0.05,10,20 = 1/F_0.95,10,20
B) F_0.05,10,20 = 1/F_0.05,20,10
C) F_0.95,10,20 = 1/F_0.05,20,10
D) F_0.95,10,20 = 1/F_0.95,20,10

Question 33

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.

Question 34

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.

Question 35

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.

Question 36

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.

Question 37

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.

Question 38

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.

Question 39

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

Question 40

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

Question 41

We compare two population variances by examining their ____________________.

Question 42

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.
Estimate with 95% confidence the ratio of the two population variances and interpret.

Question 43

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

Question 44

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

Question 45

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.

-Can we infer at the 5% level of significance that the population variances differ?

Question 46

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

Question 47

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 completion of the program data follow:

Can the statistician conclude at the 5% significance level that the required condition is not satisfied?

Question 48

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?

Question 49

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

Question 50

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

Question 51

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.
Can she infer at the 5% significance level that the population variance of investment 1 exceeds that of investment 2?

Question 52

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.
Briefly describe what the interval estimate tells you.

Question 53

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

Question 54

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

Question 55

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

Question 56

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

Question 57

Pooling is made possible by hypothesizing (under the null hypothesis) that p₁ __________ p₂.

Question 58

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 completion of the program data follow:


-Estimate with 95% confidence the ratio of the two population variances and interpret.

Question 59

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

Question 60

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.
Estimate with 95% confidence the ratio of the two population variances.

Question 61

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.


-What is the p-value of the test? Explain how to use it for testing the hypotheses.

Question 62

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.

-Estimate with 95% confidence the difference in the proportion of male and female voters who intend to vote for the Democrat candidate.

Question 63

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

Develop the 95% confidence interval estimate of the ratio of the two population variances.

Question 64

Estimate with 99% confidence the difference in the proportion of Canadians and Americans who believe that there is too much sex on television.

Question 65

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


-Explain how to use the 95% confidence interval for testing the equality of the two population variances at the 5% level.

Question 66

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?

Question 67

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.

Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2?

Question 68

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: n₁ = 400, x₁ = 208, n₂ = 250, and x₂ = 115, where x₁ and x₂ represent the number of patients in the two samples (men vs. women) who reported to have drowsiness as a result of taking headache medicine.

-Estimate with 90% confidence the difference between the two population proportions.

Question 69

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.


-Estimate with 95% confidence the difference in population proportions.

Question 70

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


-Determine the rejection region for testing the equality of the two population variances at $\alpha$ = 0.05.

Question 71

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: n₁ = 400, x₁ = 208, n₂ = 250, and x₂ = 115, where x₁ and x₂ represent the number of patients in the two samples (men vs. women) who reported to have drowsiness as a result of taking headache medicine.

-What conclusion can we draw at the 10% significance level?

Question 72

Briefly explain what the interval estimate tells you.

Question 73

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.
What is the p-value of the test?

Question 74

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


-Calculate the value of the test statistic for testing the equality of the population variances, and write the proper conclusion.

Question 75

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.

-Can the statistician infer at the 5% significance level that efforts to promote safety have been successful?

Question 76

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.
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?

Question 77

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?

Question 78

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.

-What is the p-value of the test? Explain how to use it for testing the hypotheses.

Question 79

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.

-Explain how to use the interval estimate to test the hypotheses.

Question 80

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

State the null and alternative hypotheses for determining if the population variances differ for Antioxidants A and B.