8B

1. A researcher investigated some of the variables related to "fast starts," the acceleration and speed of a hockey player from a stopped position. Sixty-eight hockey players, varsity and intramural, from a certain university were included in the experiment. Each player was required to move as rapidly as possible from a stopped position to cover a distance of 6 meters. The mean and standard deviation of the 68 individual average acceleration measurements over the 6-meter distance were 2.712 and 0.559 m/s², respectively. (a) Find a 95% confidence interval (in m/s²) for this population mean. (Round your answers to three decimal places.)(b) Suppose you were dissatisfied with the width of this confidence interval and wanted to cut the interval in half by increasing the sample size. How many skaters (total) would have to be included in the study? (Round your answer up to the nearest whole number.)
2. In a study to establish the absolute threshold of hearing, 70 male college freshmen were each seated in a soundproof room and a 150 H tone was presented at a large number of stimulus levels in a randomized order. The student was asked to press a button if he detected the tone; the experimenter recorded the lowest stimulus level at which the tone was detected. The mean for the group was 22.9 dB with s = 2.5. (a) Estimate the mean absolute threshold for all college freshmen. (b) Calculate the 95% margin of error (in dB). (Round your answer to two decimal places.)
3. Partly because of our lifestyles and the availability of fast food, the average American consumes 33.9 pounds of cheese, 12.1 pounds of ice cream, and drinks 39.5 gallons of soda each year.? Suppose that we test the accuracy of these reported averages by selecting a random sample of 40 consumers, and recording the following summary statistics.

Cheese Ice Cream Soda (lbs/yr) (lbs/yr) (gal/yr) Sample Mean 34.8 11.5 40.2 Sample Standard Deviation 1.5 3.7 6.3