Exam 9: Testing the Difference Between Two Means, Two Variances, and Two Proportions

The standard deviation of the difference in means of two large samples is .

A poll found that 37% of male voters and 42% of female voters support a particular candidate. To test whether this candidate has equal levels of support between male and female voters, the alternative hypothesis should be

A sociologist expects the life expectancy of people in Africa is different than the life expectancy of people in Asia. The data obtained is shown in the table below. Determine the 95% confidence interval for the difference in the population means.

A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and men. At = 0.05, what is an appropriate test value?

Use the following to answer questions A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X₁ and X₂ as given in the table. Consequently, D = X₁-X₂. -What critical value should be used at α = 0.05?

If the test value for the difference between the means of two large samples is 1.43 when the critical value is 1.96, the null hypothesis should not be rejected.

A marketing firm asked a random set of married and single men how much they were willing to spend on a vacation. Is there sufficient evidence at α = 0.05 to conclude that is there a difference in the two amounts?

When the subjects are paired or matched in some way, samples are considered to be _______________.

A medical researcher is interested in whether patients' left arms or right arms are longer. If 10 patients participate in this study, how many degrees of freedom should the researcher use when finding the critical value for a t test?

Use the following to answer questions A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X₁ and X₂ as given in the table. Consequently, D = X₁-X₂. -Determine the mean of the differences.

In comparing the two standard deviations below, what test value and degrees of freedom should be used in an F test?

A bond analyst is analyzing the interest rates for equivalent municipal bonds issued by two different states. At α = 0.05, is there enough evidence to conclude that there is a difference in the interest rates paid by the two states?

Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 17 of 50 at one school and 15 of 30 at the other have ear infections. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools?

Two groups were polled about their attitudes towards capital punishment. In one group 30 out of 100 favored capital punishment, and in the other group 40 out of 80 favored capital punishment. Calculate an appropriate test value test the hypothesis that the population proportions are the same.

Use the following to answer questions A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. -What is the test value?

What is the critical value for a two-tailed F test with α = 0.10, when the sample size from which the variance for the numerator was obtained is 10, and the sample size from which the denominator was obtained is 24?

When finding the test value for an F test, the smaller of the two variances should be placed in the numerator.

The average credit card debt for a recent year was $9540. Five years earlier the average credit card debt was $8880. Assume sample sizes of 34 were used and the population standard deviations of both samples were $1069. Is there evidence to conclude that the average credit card debt has increased? Use . a. State the hypotheses. b. Find the critical value. c. Compute the test statistic. d. Make the decision. e. Summarize the results.

To determine whether two sample variances are equal, a researcher can use a(n) __________.

Use the following to answer questions A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. -Calculate the critical value. Use α = 0.05.