Sometimes only summary data is available for a variable of interest. If you are conducting a hypothesis test, you can use R to determine the p-value, but you must do the remainder of the test by hand. If you are constructing a confidence interval, you can use R to determine /2 or /2, for your given , but you must perform the remaining calculations by hand. Use R commander to assist you (which only provide summary data and not a dataset).

A random sample of size 16 is taken from a normal population with a known standard deviation of 2. The sample mean is 15. Complete the following questions using hand calculations but use R commander (instead of statistical tables) to obtain the p-value and critical values. Remember to paste relevant output into your solutions.

a) Is there evidence that the population mean differs from 16? Test using the 5% level of significance. Complete all 6 steps of your hypothesis test, including a discussion of the assumptions.

b) Construct a 99% confidence interval for the population mean . Do you have evidence that the true population mean differs from 16? Explain. c) If you've done all calculations correctly, your conclusions in parts (a) and (b) should disagree: one approach provided sufficient evidence to suggest 16, while the other approach provided insufficient evidence 16. Explain why this is the case.

Beer21.xlsx: https://docs.google.com/spreadsheets/d/1vfm6fBr1RVDyaCESVeWa7NT34XWyloLE/edit?usp=sharing&ouid=115230153487011463694&rtpof=true&sd=true

School100.xlsx: https://docs.google.com/spreadsheets/d/1gMUnbRKXO66hv5FcBCHL2P_cF5rJrXkA/edit?usp=sharing&ouid=115230153487011463694&rtpof=true&sd=true