Chapter 10 Review Mab

Use Scenario 10-10. Which of the following is a 98% confidence interval forU2-U1 (using the conservative value for the degrees of freedom)?

(-2.40, 12.80)

Use Scenario 10-4. A 99% confidence interval for p1 - p2 is

. (-0.354, 0.114)

We wish to test the hypothesis that the mean difference in time to sort the beads with and without music is 0. Which of the following is the appropriate test statistic?

0.4/1.96 Square root 15

Scenario 10-2 An SRS of 100 flights by Nite-flite Airlines showed that 64 were on time. An SRS of 100 flights by Waxwing Airlines showed that 80 were on time. Let pN be the proportion of on-time flights for all Nite-flite Airline flights, and let pW be the proportion of all on-time flights for all Waxwing Airlines flights. Use Scenario 10-2. A 95% confidence interval for the difference pA - pW is

(-0.283, -.0.038)

Use Scenario 10-9. Which of the following is a 99% confidence interval for U1 - U2 (using the conservative value for the degrees of freedom)?

(-7.2,15.2)

Scenario 10-1 In a large Midwestern university (with the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in 1993 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 1997, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let p1 be the proportion of all entering freshmen in 1993 who graduated in the bottom third of their high school class, and let p2 be the proportion of all entering freshmen in 1997 who graduated in the bottom third of their high school class. ____ 7. Use Scenario 10-1. Which of the following represents 99% confidence interval for p1 - p2?

D

Use Scenario 10-8. Assuming the conditions for using t-procedures have been met, which of the following represents a 90% confidence interval for U1-U2 (using a conservative value for the degrees of freedom).

D.

Scenario 10-3 A manufacturer receives parts independently from two suppliers. An SRS of 400 parts from supplier 1 finds 20 that are defective. An SRS of 100 parts from supplier 2 finds 10 that are defective. Let p1 and p2 be the proportions of all parts from suppliers 1 and 2, respectively, that are defective. ____ 12. Use Scenario 10-3. Which of the following represents a 95% confidence interval for p1 - p2?

-0.05+- 1.96

Use Scenario 10-4. Is there evidence of a decrease in the proportion of tomatoes suffering frost damage for tomatoes sprayed with kelp extract? To determine this, you test the hypotheses H0: p1 = p2, Ha: p1 < p2. The P-value of your test is A. greater than 0.10. B. between 0.05 and 0.10. C. between 0.01 and 0.05. D. between 0.001 and 0.01. E. below 0.001.

. between 0.05 and 0.10.

At a large state university, the heights of male students who are interscholastic athletes is approximately Normally distributed with a mean of 74.3 inches and a standard deviation of 3.5 inches. The heights of male students who don't play interscholastic sports (we'll call them "non-interscholastics") is approximately Normally distributed with a mean of 70.3 inches and a standard deviation of 3.2 inches. You select an SRS of 10 interscholastic athletes and 12 non-interscholastics. What is the probability that the sample mean of non-interscholastics is greater than the sample mean of interscholastic athletes? A. nearly 0 B. 0.0027 C. 0.0035 D. 0.9965 E. 0.9973

0.0027

You have two large bins of marbles. In bin A, 40% of the marbles are red. In bin B, 52% of the marbles are red. You select a simple random sample of 30 marbles from bin A and 40 marbles from bin B. What is the probability that the proportion of red marbles in the sample from bin A is greater than the proportion of red marbles from bin B? A. nearly zero B. 0.0010 C. 0.1190 D. 0.1357 E. 0.1562

0.1562

Use Scenario 10-7. Suppose we wished to determine if there tended to be a significant difference in mean height for the seedlings treated with the different herbicides. To answer this question, we decide to test the hypotheses H0:Ub-Ha=0 vs. Ha:Ub-Ua not = 0 Based on our data, which of the following is the value of test statistic? A. 14.60 B. 7.80 C. 3.43 D. 2.54 E. 1.14

3.43

An SRS of 100 is taken from a Normal distribution with a mean of 25 and a standard deviation of 4, and an SRS of 85 is taken from a different Normal distribution with a mean of 40 and a standard deviation of 7. Which of the following expressions represents the standard deviation of the sampling distribution of the difference of means from these two samples?

A

Use Scenario 10-6. Let p1 = proportion of couples that had a child within the first three years and were divorced within five years and p2 = proportion of couples that did not have a child within the first three years and were divorced within five years. We wish to test the hypotheses Ho:p1-p2=0 vs. Ha:p1-p2>0 . Which of the following is the appropriate expression for the test statistic?

A

Scenario 10-5 An SRS of 45 male employees at a large company found that 36 felt that the company was supportive of female and minority employees. An independent SRS of 40 female employees found that 24 felt that the company was supportive of female and minority employees. Let p1 represent the proportion of all male employees members at the company and p2 represent the proportion of all female employees members at the company who hold this opinion. We wish to test the hypotheses Ho: p1-p2=0 vs. Ho: p1-p2>0 ____ 17. Use Scenario 10-5. Which of the following is the correct expression for the test statistic?

B

According to recent polls, 24% of people in the United States answered Yes to the question, "Did you smoke any form of tobacco yesterday?" In the European Union, 28% of people answered yes to a similar question. Let's assume these are population parameters for the two populations. If you select a simple random sample of 40 people in the U.S. and 50 people in the E.U., which of the following expressions represents the standard deviation of the sampling distribution for the difference in the proportion of smokers in the two groups?

C.

Use Scenario 10-7. A 95% confidence interval for Ub-Ua is given by which of the following expressions? (Use the conservative value for degrees of freedom.)

C.

Use Scenario 10-5. The P-value for this test is 0.0217. Which of the following is a correct conclusion? A. Reject H0 at = 0.01: we have evidence that the proportion of male employees who feel that the company is supportive of women and minority employees is higher than the proportion of women who feel this way. B. Reject H0 at = 0.01: we do not have evidence that the proportion of male employees who feel that the company is supportive of women and minority employees is higher than the proportion of women who feel this way. C. Accept H0 at = 0.01: we do not have evidence that the proportion of male employees who feel that the company is supportive of women and minority employees is higher than the proportion of women who feel this way. D. Accept Ha at = 0.01: we do not have evidence that the proportion of male employees who feel that the company is supportive of women and minority employees is higher than the proportion of women who feel this way. E. Fail to reject H0 at = 0.01: we do not have evidence that the proportion of male employees who feel that the company is supportive of women and minority employees is higher than the proportion of women who feel this way.

Fail to reject H0 at = 0.01: we do not have evidence that the proportion of male employees who feel that the company is supportive of women and minority employees is higher than the proportion of women who feel this way.

Use Scenario 10-9. The sportswriter wishes to test the hypotheses Ho:U1-U2=0 vs. Ha: U1-U2>0 The P-value for the test (using the conservative value for the degrees of freedom) is 0.132. Which of the following is the appropriate conclusion to draw from this test, if = 0.05? A. Accept Ha B. Reject Ha C. Reject H0 D. Fail to reject Ha E. Fail to reject H0

Fail to reject Ho

Use Scenario 10-10. The researcher decides to test the hypotheses H0:U2-U1=0 vs. Ha:U2-U1>0 at the a = 0.05 level and produces a P-value of 0.0475. Which of the following is a correct interpretation of this result? A. The probability that the difference is 0.0475. B. The probability that this test resulted in a Type II error is 0.0475. C. If this test were repeated many times, we would make a Type I error 4.75% of the time. D. If the null hypothesis is true, the probability of getting a difference in sample means as far or farther from 0 as the difference in our samples is 0.0475. E. If the null hypothesis is false, the probability of getting a difference in sample means as far or farther from 0 as the difference in our samples is 0.0475.

If the null hypothesis is true, the probability of getting a difference in sample means as far or farther from 0 as the difference in our samples is 0.0475.

11. Use Scenario 10-2. Is there evidence of a difference in the on-time rate for the two airlines? To determine this, you test the hypotheses H0: p1 = p2, Ha: p1 p2. The P-value of your test is 0.0117. Which of the following is an appropriate interpretation of the P-value? A. If the on-time rates for the two airlines are equal, the probability of getting samples with a difference as far or farther from zero as these samples is 0.0117. B. If the on-time rates for the two airlines are not equal, the probability of getting samples with a difference as far or farther from zero as these samples is 0.9883. C. The probability of making a Type I error is 0.0117. D. The probability of making a Type II error is 0.0117. E. The probability that H0 is true is 0.0117.

If the on-time rates for the two airlines are equal, the probability of getting samples with a difference as far or farther from zero as these samples is 0.0117

Use Scenario 10-4. In the original design for this experiment, 50 tomato plants were grown in one large container and 50 more were grown in a second container. The plants in container 1 were sprayed with kelp extract and the plants in container 2 were not. Why would z-procedures for confidence intervals and tests of significance be of questionable value in this situation? A. We cannot be sure that the Normality condition has been met. B. We don't know whether the 10% condition has been met. C. Individual plants were not assigned randomly to the two experimental treatments—any influence of kelp extract is confounded with differences between the two containers. D. Because we don't know the standard deviation for either population, we shouldn't use z-procedures. E. We are collecting results on the entire population of plants, so statistical inference from samples is unnecessary.

Individual plants were not assigned randomly to the two experimental treatments—any influence of kelp extract is confounded with differences between the two containers.

Use Scenario 10-10. The P-value in the previous question was produced by a calculator, using the software estimate of 43.97 degrees of freedom. If we used the more conservative value of the smaller of (n2-1) or (n2-1), how would the P-value change for the same data? A. It would be smaller. B. It would be larger. C. It would not change, since the test statistic's value is not influenced by the degrees of freedom. D. Since the P-value depends on the value of a random variable (the sample mean), we can't predict whether it will be larger, smaller, or the same. E. Whether it's larger, smaller, or the same depends on what level of significance we choose.

It would be larger.

Use Scenario 10-8. If we had used the more accurate software approximation for the degrees of freedom, how would the 90% confidence interval compare to the one we constructed with the more conservative value for degrees of freedom? A. It would be wider. B. It would be narrower. C. It would not change. D. Whether it would be wider, narrower, or stay the same depends on the sample sizes. E. Since t confidence intervals are constructed with sample standard deviations, we don't know whether it would be wider, narrower, or the same.

It would be narrower.

According to Humane Society data, 39% of households in the United States have at least one dog. In the United Kingdom, 23% of households have at least one dog. Suppose you select an SRS of 75 households in the U.S. and 80 households in the U.K., and calculate = the proportion of households in the U.S. sample that have a dog, and = the proportion of households in the U.K. sample that have a dog. Which of the following best describes the sampling distribution of proportions for P^1 - P^2 ? A. Mean = 0.16, Standard deviation = 0.024, Shape unknown B. Mean unknown, Standard deviation unknown, Shape approximately Normal. C. Mean = 0.16, Standard deviation = 0.024, Shape unknown D. Mean unknown, Standard deviation unknown, Shape approximately Normal. E. Mean = 0.16, Standard deviation = 0.073, Shape approximately Normal.

Mean = 0.16, Standard deviation = 0.073, Shape approximately Normal.

A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a standard deviation of 4.2 years. The distribution of life spans for electric ranges has a mean of 13.4 years and a standard deviation of 3.7 years. Both distributions are moderately skewed to the right. Suppose we take a simple random sample of 35 gas ranges and a second SRS of 40 electric ranges. Which of the following best describes the sampling distribution of X_G - X_E, the difference in mean life span of gas A. Mean = 1.6 years, standard deviation = 7.9 years, shape: moderately right-skewed. B. Mean = 1.6 years, standard deviation = 0.92 years, shape: approximately Normal. C. Mean = 1.6 years, standard deviation = 0.92 years, shape: moderately right skewed. D. Mean = 1.6 years, standard deviation = 0.40 years, shape: approximately Normal. E. Mean = 1.6 years, standard deviation = 0.40 years, shape: moderately right skewed.

Mean = 1.6 years, standard deviation = 0.92 years, shape: approximately Normal.

Use Scenario 10-8. Which of the following would lead us to believe that the t-procedures were not safe to use in this situation? A. The sample medians and means for the two groups were slightly different. B. The distributions of the data for the two groups were both slightly skewed right. C. The data are integers between 1 and 10 and so cannot be normal. D. The standard deviations from both samples were very different from each other. E. None of the above.

None of the above.

An experiment to test the effectiveness of regular treatments with fluoride varnish to reduce tooth decay involved 36 volunteers who had half of their teeth—the right side or left side, determined by a coin flip—painted with a fluoride varnish every six month for 5 years. At the end of the treatments, the number of new cavities during the treatment period was compared on treatment (fluoride varnish) side versus the control (no fluoride varnish) side. The appropriate statistical test for analyzing the results of this experiment is A. One-sample z-test of proportions. B. Two-sample z-test for difference of proportions. C. One-sample t-test on paired data. D. Two-sample t-test for difference of means. E. Two-sample z-test for difference of means.

One sample t-test on paired data

Use Scenario 10-1. Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 1997 has been reduced as a result of the tougher admission standards adopted in 1995, compared to the proportion in 1993? To determine this, you test the hypotheses H0: p1 = p2, Ha: p1 > p2 at the = 0.05 level. You calculate a test statistic of 1.980. Which of the following is the appropriate P-value and conclusion for your test? A. P-value = 0.047; fail to reject H0; we do not have evidence that the proportion who graduated in the bottom third of their class has been reduced. B. P-value = 0.047; accept Ha; there is evidence that the proportion who graduated in the bottom third of their class has been reduced. C. P-value = 0.024; fail to reject H0; we do not have evidence that the proportion who graduated in the bottom third of their class has been reduced. D. P-value = 0.024; reject H0; we have evidence that the proportion who graduated in the bottom third of their class has been reduced. E. P-value = 0.024; fail to reject H0; we have evidence that the proportion who graduated in the bottom third of their class has not changed.

P-value = 0.024; reject H0; we have evidence that the proportion who graduated in the bottom third of their class has been reduced.

Use Scenario 10-1. Which of the following best explains why it was important to know that the university had 6000 or more entering freshman before using z-procedures in this situation? A. If the size of the freshman classes were much smaller, we could not be confident that the Normality condition for these procedures had been met. B. The central limit theorem would not apply if the population size was below 500. C. To meet the independence condition for this procedure, we needed to know that the samples were less than 10% of the population size. D. To meet the random condition for this procedure, we needed to know that the samples were less than 10% of the population size. E. The information about the size of the Freshman classes was not important, it was added to the problem simply to provide extraneous numbers.

To meet the independence condition for this procedure, we needed to know that the samples were less than 10% of the population size.

Use Scenario 10-3. Suppose the 95% confidence interval for the difference in the proportion of defective parts from the two suppliers is . Which of the following is the best interpretation of the confidence interval? A. 95% of the time, the true difference in the proportion of defective parts from the two suppliers is in the interval . B. We are 95% confident that the true difference in the proportion of defective parts from the two suppliers is in the interval . C. The probability that the true difference in the proportion of defective parts from the two suppliers is in the interval is 95%. D. We are 95% confident that the interval captures the true difference in the proportion of defective parts from the two suppliers. E. 95% of the differences calculated from samples this size will be in the interval .

We are 95% confident that the interval (a,b) captures the true difference in the proportion of defective parts from the two suppliers.

Use Scenario 10-10. Which of the following is a correct interpretation of this interval? A. 98% of the time, the true difference in the mean heart rate of subjects in the high-step vs. low-step groups will be in this interval. B. We are 98% confident that this interval captures the true difference in mean heart rate of subjects in the high-step vs. low-step groups. C. There is a 0.98 probability that the true difference in mean heart rate of subjects in the high-step vs. low-step groups in this interval. D. 98% of the intervals construction this way will contain the value 0. E. There is a 98% probability that we have not made a Type I error.

We are 98% confident that this interval captures the true difference in mean heart rate of subjects in the high-step vs. low-step groups.

Use Scenario 10-6. The P-value for this one-sided test is 0.0314. If a = 0.05, which of the following is the best conclusion? A. there is evidence of an association between divorce rate and having children early in a marriage. B. having more children increases the risk of divorce during the first 5 years of marriage. C. If you want to decrease your chances of getting divorced, it is best to marry later in life. D. If you want to decrease your chances of getting divorced, it is best not to have children. E. If you want to decrease your chances of getting divorced, it is best to wait several years before having children.

there is evidence of an association between divorce rate and having children early in a marriage

The 90% confidence interval for the difference is Ub-Ua 14.6 ± 7.80. We wish to test the hypotheses H0:Ub-Ua=0 vs. Ha:Ub-Ua not=0 . Based on this confidence interval A. we would not reject H0 at the 0.10 level. B. we would reject H0 at the 0.10 level. C. we would not reject H0 at the 0.05 level. D. we would reject H0 at the 0.05 level. E. we would accept Ha at the 0.10 level.

we would reject H0 at the 0.10 level.