A researcher records the repair cost for 14 randomly selecte

A researcher records the repair cost for 14 randomly selected stereos. A sample mean of $80.46 and standard deviation of $19.18 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the stereos. Assume the population is normally distributed. CONFIDENCE INTERVAL Find the critical value that should be used in constructing the confidence interval. Answer: (Round answer to 3 decimal places) Construct the 95% confidence interval. Lower Bound: (Round answer to 2 decimal places) Upper Bound:

Solution

(A) The degree of freedom =n-1=14-1=13

Given a=1-0.95=0.05, the critical value is t(0.025, df=13) = 2.160 (from student t table)

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(B) So the lower bound is

xbar - t*s/vn =80.46-2.16*19.18/sqrt(14) = 69.39

So the upper bound is

xbar +t*s/vn=80.46+2.16*19.18/sqrt(14) =91.53