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Nitterhouse Masonry Products, LLC, in Chambersburg,Pennsylvania, produces architectural concrete masonry products. TheDover, the largest block in a certain collection, is used primarilyfor residential retaining walls, and is manufactured to weigh 45pounds. A quality control inspector for the company randomlyselected 17 blocks, and determined that they have an average weightof 46.6 pounds with a sample standard deviation of 3.20 pounds.Assume that the distribution of the weights of the blocks isnormal. Please use 4 decimal places for all critical values.

(0.5 pts.) a) Should a z or t distribution be used forstatistical procedures regarding the mean? Please explain youranswer.

b) Is there any evidence to suggest that the true mean weight isnot 45 pounds at a 5% significance level?

Calculate the test statistic

Calculate the p-value.

Write the complete four steps of the hypothesis test below. Thework for all parts will be at the end of the question.

c) Calculate the 95% confidence interval for the mean.

d) Explain why parts b) and c) state the same thing. That is,what in part b) is consistent with what in part c)?

e) Is there strong evidence for your decision of \"reject thenull hypothesis\" or \"fail to reject the null hypothesis\"? Pleaseexplain your answer using the results from both the hypothesis testand the confidence interval.