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TMS is a brand of designer T-shirts that is highly popular amongst the teenagers. The manufacturer suspects that its retailers charge less than the recommended retail price of $60. A market research company was engaged to investigate the matter and collected data from 66 randomly selected retailers. The mean retail price calculated from the sample is found to be $59 with a standard deviation $5.20. Assuming that retail prices of the T-shirts are normally distributed, estimate with 95% confidence the actual mean retail price of the T-shirts.
a) Suppose you were a junior statistician working for the market research company. Which formula would you select to use in solving the problem? Provide a brief reason on your selection.
b) Obtain the lower confidence limit and the upper confidence limit of the 95% confidence interval estimate of the actual mean retail price of the T-shirts. Display working.
c) Present an interpretation of the lower confidence limit and the upper confidence limit obtained in part b) in the context of the problem.
d) Does the result of the estimation you just completed fully support the suspicion of the manufacturer? Yes or no? Why? Present your reasoning.
What would happen to the width of the interval when a higher confidence level is used? Assume all of the other variables to do the calculation of confidence interval held constant.
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