A machine produces metal rods used in an automobile suspension system. A random

Question

A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected, and the diameter is measured. The resulting data (in millimeters) are as follows: 8.24, 8.21, 8.23, 8.25, 8.26, 8.23, 8.20, 8.26, 8.19, 8.23, 8.20, 8.28, 8.24, 8.25, 8.24 We can assume that the rod diameter is normally distributed. a. Compute the sample mean and the sample variance. b. Using the statistics from part a compute a 95% confidence interval for the mean diameter. c. Suppose that these data are from a preliminary study that will be used to obtain an estimate of the standard deviation of the diameter. Using the sample standard deviation s as the true standard deviation sigma, compute the required sample size to be 95% confident that the maximum error of the estimate is at most 0.01 when using the sample mean to estimate the population mean.

Explanation / Answer

a) mean =8.2340

sample variance = 0.00064

b)for 95% CI and (n-1=14) degree of freedom ; t=2.1448

therefore 95% confidence interval =sample mean -/+ t*std error =8.2200 ; 8.2480

c) here std deviation=0.0253

for 95% confidence interval ; z=1.96

margin of error E =0.01

therefore sample size n=(z*std deviation/E)2 =~25

X 8.24 8.21 8.23 8.25 8.26 8.23 8.2 8.26 8.19 8.23 8.2 8.28 8.24 8.25 8.24 mean(X) 8.2340 std deviation(S) 0.0253 std error =S/(n)1/2 0.0065

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