The melting point of each of 16 samples of a certain brand of vegetable oil was determined,
resulting in bar = 94.32. Assume that the distribution of the melting point is normal with = 1.2.

a) Test whether the true melting point of vegetable oil differs from 94 using a significance
level of = 0.05. Clearly show all 8 steps of the hypothesis test, including both the rejection
regions and the p-value. (10)

b) Would the conclusion in a) remain the same if a significance level of 0.01 is used instead
of 0.05? Motivate your answer. (2)

c) In general, a p-value is … (1)

d) Referring to the information given in a), what is the probability of making a Type I error?
Also interpret a Type I error in terms of this example.