Question: A random sample of 172 students was asked to rate on a scale to from 1 (not important) to 5 (extremely important) health benefits as a job characteristic (note that the rating scale can also have decimals, i.e. a student can give a rating of 1.32). The sample mean rating was 3.31, and the sample standard deviation was 0.70.

a) Obtain a 95% confidence interval for the mean rating. And explain what the interval represents.

b) For a type I error of 1%, can you be reasonably certain that the average rating is more than 3 in the population? Please state your hypothesis clearly (both verbally and symbolically).Also briefly explain the testing procedure (namely what type of test you will be using, how you would calculate your test statistic, p-value and the rejection criteria).

c) Obtain a 99% confidence interval for the mean rating. Can you use the 99% confidence interval to test the hypothesis from part b? Why or why not?

d) What assumption(s) do you need to make in order answer the above questions?