2. A baker is concerned that his chocolate chip cookies weigh less, on average, than their
advertised weight of 50 grams each, and that he will lose customers as a result. Assume that
cookies’ weights (in grams) are independent and distributed as (, ).
a) (5 marks) The baker guesses from historical data that is at most 3. He considers a mean
weight of less than 48 grams to be problematic. What is the minimum number of cookies
that he will need to weigh in order to be able to detect < 50 with probability 80%
(assuming a significance level of 5%)?
b) (5 marks) The baker asks a student to collect measurements of 25 cookies’ weights and to
record them in the file cookies.txt. Conduct a hypothesis test of whether the mean
cookie weight is less than 50 grams. Be sure to state your null and alternative hypotheses,
test statistic, critical value, and conclusion. Use a significance level of 5%.
c) (2 marks) Refer to the test in b). Would a Type I or Type II error be more serious in this
setting? Why?
