### Weight 49 49 3 48 49 (1)

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?