3. (21 marks) A study by a researcher in a lab is to address the question of whether the mean body temperature of humans is 37. The body temperatures of six graduate students in the lab were measured {35.5, 36, 37.5, 35, 36.5, 37.8}. Note that the sample mean is = 36.383. Assume that the standard deviation of the body temperatures of humans is 0.5.

a) Test at the 5% significance level whether the average body temperature of humans is different from 37. Complete your hypothesis test, including a discussion of the assumptions. (8 marks)

b) Obtain and interpret a 90% two-sided confidence interval for the mean body temperature of humans. (6 marks)

c) Does the interval in part (b) give evidence that the average body temperature of humans differs from 37? Explain. (3 marks)

d) In order for the above inferences to be valid, it is necessary for us to assume the sample is randomly selected from a normally distributed population. Are there any indications that either of these assumptions are violated? Explain. Hint: To check one of these assumptions, you will find it helpful to construct a histogram or a stem-and-leaf display. (4 marks).