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 with questions 3 and 4 (which only provide summary data and not a dataset).

A random sample of size 16 is taken from a normal population. The sample mean is 15 and the sample standard deviation is 2. 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 exceeds 13? 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 12.8? Explain

c) The above inferences are performed using a sample of size 16, randomly selected from a normal population. As such, the above inferences were valid.

i. Would one mean inference be valid if a sample of size 50 was obtained from a normally distributed population? Explain.

ii. Would one mean inference be valid if a sample of size 16 was obtained from a strongly skewed population? Explain.

iii. Would one mean inference be valid if a sample of size 50 is obtained from a strongly skewed population? Explain.

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