MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

**Solve the problem.**

10) We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each brand of cola at each supermarket. The data are shown in the following table:

Find a 98% confidence interval for the difference in mean price of brand 1 and brand 2.

A) 0.0375 ± 0.0404 B) 0.0375 ± 0.1393 C) 0.0375 ± 0.0471 D) 0.0375 ± 0.0347

11) Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labeled A and B) and recorded the prices charged by each supermarket. The summary results are provided below:

*x*A = 2.09 *x*B = 1.99 *d *= .10

*s*A = 0.22 *s*B = 0.19 *sd *= .03

Assuming the data represent a matched pairs design, calculate the confidence interval for comparing mean prices using a 95% confidence level.

A) .10 ± .00588 B) .10 ± .056975 C) .10 ± .1255 D) .10 ± .004935

12) A researcher is investigating which of two newly developed automobile engine oils is better at prolonging the life of an engine. Since there are a variety of automobile engines, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Suppose the following 95% confidence interval for *μ*A –

*μ*B was calculated: (100, 2500). Which of the following inferences is correct?

A) We are 95% confident that an engine using oil A has a higher mean number of hours of continuous use before breakdown than does an engine using oil B.

B) We are 95% confident that the mean number of hours of continuous use of an engine using oil A is between 100 and 2500 hours.

C) We are 95% confident that an engine using oil B has a higher mean number of hours of continuous use before breakdown than does an engine using oil A.

D) We are 95% confident that no significant differences exists in the mean number of hours of continuous use before breakdown of engines using oils A and B.

13) An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the

new coating, the inventor randomly selects one of the two tires on each of 50 bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to determine whether the new spray coating improves the wear of the bicycle tires. The data and summary information is shown below:

Use the summary data to construct a 90% confidence interval for the difference between the means.

A) 0.53 ± 0.01663 B) 0.53 ± 0.04512 C) 0.53 ± 0.01396 D) 0.53 ± 0.03787

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

14) A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let *μ*1 be the true mean weight of individuals before starting the diet and let *μ*2 be the true mean weight of individuals after 3 weeks on the diet.

Person Weight Before Diet Weight After Diet

1 166 159

2 211 206

3 204 201

4 213 207

5 220 216

Summary information is as follows: *d *= 5, *sd *= 1.58. Calculate a 90% confidence interval for the difference between the mean weights before and after the diet is used.

15) The data for a random sample of five paired observations are shown below.

Pair Observation 1 Observation 2

1 3 5

2 4 4

3 3 4

4 2 5

5 5 6

a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1. Use the differences to calculate *d *and *sd*.

b. Calculate the means *x*1 and *x*2 of each column of observations. Show that

*d **= **x*1 – *x*2.

c. Form a 90% confidence interval for *μD.*

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