Question 1. A manager at a manufacturing plant wants to investigate the quality of his employee's work after one employee says that he thinks some of the other employees need retraining. The manager has been saying that the average number of acceptable parts coming from their department is 90%. He collects data over a two-week window on 100 employees to test if the number of acceptable parts is less than 90% at a 0.05 level of significance. If it is less than 90%, he feels compelled to implement a retraining program.

DATA 65 36 49 84 79 56 28 43 67 36 43 78 37 40 68 72 55 62 22 82 88 50 60 56 57 46 39 57 73 65 59 48 76 74 70 51 40 75 56 45 35 62 52 63 32 80 64 53 74 34 76 60 48 55 51 54 45 44 35 51 21 35 61 45 33 61 77 60 85 68 45 53 34 67 42 69 52 68 52 47 62 65 55 61 73 50 53 59 41 54 41 74 82 58 26 35 47 50 38 70 (a) Compute the mean and standard deviation of the number of acceptable parts (b) Which type of test we should use? Parametric vs Non-parametric? Please justify your conclusion. (c) Conduct the appropriate hypothesis test if there is enough evidence to show the average number of acceptable parts is less than 90%. (Write our hypotheses, test statistics, p-value, decision and conclusion.) (d) Explain what a type I and type II error would be in terms of implementing a retraining program and whether the program is actually needed.

Question 2. A manufacturer of a certain brand of rice cereal claims that the average saturated fat content does not exceed 1.5 grams per serving. State the null and alternative hypotheses to be used in testing this claim and determine where the critical region is located.