Probability and Statistics (Answer up to 7th decimal point**)

And please give the answer step-by-step as I want to know how to calculate the answer, thanks.

Q4. (14%) Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed. A random sample of 15 teenagers was drawn and each reported the amount of time spent at part-time jobs (in minutes). These are listed here.

180 & 130 & 150 & 165 & 90 & 130 & 120 & 60 & 200 & 180 & 80 & 240 & 210 & 150 & 125

(a) Given that the margin of error for the population mean is 27.7064, determine the corresponding critical value. What is the associated significance level?

(b) Based on (a), determine the associated confidence interval estimate of the population mean. State clearly the level of confidence in this problem.

(c) Determine the 90% confidence interval estimate of the population variance.

(d) Give an interpretation for the confidence intervals in (b) and (c).