Type I or Type II error

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2. A baker is concerned that his chocolate chip cookies weigh less, on average, than theiradvertised weight of 50 grams each, and that he will lose customers as a result. Assume thatcookies’ 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 meanweight of less than 48 grams to be problematic. What is the minimum number of cookiesthat 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 torecord them in the file cookies.txt. Conduct a hypothesis test of whether the meancookie 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 thissetting? Why?

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