A process for producing vinyl floor covering has been stable for a long period. The surface hardness measurement of the flooring is normally distributed with a mean of 5 and a standard deviation of...

A process for producing vinyl floor covering has been stable for a long period. The surface hardness measurement of the flooring is normally distributed with a mean of 5 and a standard deviation of 1.52. Suppose a new crew of workers have been hired and trained. To monitor the production of the new crew, a random sample of 21 vinyl specimens are measured for hardness. The sample yields an average of 5.24.
Calculate the 90% confidence interval for the average hardness of vinyl.

Suppose the engineer would like the entire 90% confidence interval to be no wider than 0.5 units. What is the smallest sample size needed to obtain the desired margin of error?

Based on the 90% confidence interval, is there evidence to say that the population mean surface hardness was more than 5? Explain your answer.