Calculate a ninety percent confidence interval for m

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Reference no: EM13909919

THE DISK BRAKE CASE

National Motors has equipped the ZX-900 with a new disk brake system. We define the stopping distance for a ZX-900 to be the distance (in feet) required to bring the automobile to a complete stop from a speed of 35 mph under normal driving conditions using this new brake system. In addition, we define m to be the mean stopping distance of all ZX-900s. One of the ZX-900's major competitors is advertised to achieve a mean stopping distance of 60 feet. National Motors would like to claim in a new advertising campaign that the ZX-900 achieves a shorter mean stopping distance.

Suppose that National Motors randomly selects a sample of n = 81 ZX-900s. The company records the stopping distance of each automobile and calculates the mean and standard deviation of the sample of n = 81 stopping distances to be x = 57.8 ft and s = 6.02 ft.

a. Calculate a 95 percent confidence interval for m. Can National Motors be 95 percent confident that m is less than 60 ft? Explain.

b. Using the sample of n = 81 stopping distances as a preliminary sample, find the sample size necessary to make National Motors 95 percent confident that x is within a margin of error of one foot of m.

Reference no: EM13909919

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