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

Twelve dieters lost an average of 9.8 pounds in 6 weeks when given a special diet plus a "fat-blocking" herbal formula. A control group of twelve other dieters were given the same diet, but without the herbal formula, and lost an average of 8.8 pounds during the same time. The standard deviation of the "fat-blocker" sample was 2.6 and the standard deviation of the control group was 2.8. Find the 95% confidence interval for the differences of the means.

The number of calories in a 12-ounce serving of randomly-selected regular and lite beers is listed. Is there sufficient evidence to conclude that the mean number of calories for lite beers is significantly less than that for the regular beers? Use . Assume the variables are approximately normally distributed. a.State the hypotheses. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results.

A researcher hypothesized that the variation in the car rental rates (in US$/day) at a major city airport is less than in the car rental rates down town. A survey found that the variance of the rental rates on 7 cars at the airport was 25.7 while the variance of the rental rates on 6 cars down town was 60.4. What test value should be used in a F test?

A conservationist suspects that the water level in Horseshoe Lake has been affected more by the current drought than the water level in Swan Lake, so he measures how far the water level is below normal each day in June. The data are normally distributed. Test his hypothesis at α = 0.01.

The Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town, and it is believed that the average hourly wage charged by both agencies is the same. A Donaldson manager surveyed other employers in town to find what they paid the agencies for temporary secretaries. The results are summarized below. At , test the claim that each agency charges the same hourly wage.

A group of college students believes the average grades in psychology courses are different than the average grades in biology courses. The group found the average psychology grades of a sample of 8 students was 86.4 and the average biology grades of a sample of 10 students was 82.2. What is the null hypothesis for this study?

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 an appropriate null hypothesis?

In the F distribution the mean value of F is approximately equal to __________.

In a test of the difference between the two means below, what should the test value be for a t test?

An field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at = 0.10, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?

For the samples summarized below, test the hypothesis, at α = 0.05, that the two variances are different.

Consider the null hypothesis . If the confidence interval for does not contain 0, the null hypothesis should be rejected.

Find and , if , , , and .

If the test value for the difference between the means of two large samples is 2.57 when the critical value is 1.96, what decision should be made?

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. -State the alternative hypothesis?

Find X, given and n = 28.

Determine the value of α as shown below in the graph of an F distribution. The degrees of freedom for the numerator are seven, and the degrees of freedom for the denominator are nine.

Joan has just moved into a new apartment and wants to purchase a new couch. To determine if there is a difference between the average prices of couches at two different stores, she collects the following data. Test the hypothesis that there is no difference in the average price. Use α = 0.05.

Find and , if , , , and .

The critical value for a left-tailed t test for dependent samples is ___________ when there are seven degrees of freedom and α = 0.025.