3. 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 1% level of significance. Complete all 6 steps of your hypothesis test, including a discussion of the assumptions. (7 marks)

b) Construct a 95% confidence interval for the population mean . Do you have evidence that the true population mean differs from 16? Explain. (6 marks)

c) If you've done all calculations correctly, your conclusions in parts (a) and (b) should disagree: one approach provided insufficient evidence to suggest 16, while the other approach provided sufficient evidence 16. Explain why this is the case. (2 marks)

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