Refer to Problem 26. Suppose that you decide to use a z-test with a significance level of 0.10 and a sample size of 35. Assume that σ = 6.9 lb.
a. Determine the probability of a Type I error.
b. If last year's mean cheese consumption was 36.5 lb, identify the distribution of the variable x̅, that is, the sampling distribution of the mean for samples of size 35.
c. Use part (b) to determine the probability, β, of a Type II error if in fact last year's mean cheese consumption was 36.5 lb.
d. Repeat parts (b) and (c) if in fact last year's mean cheese consumption was 33.5 lb, 34.0 lb, 34.5 lb, 35.0 lb, 35.5 lb, 36.0 lb, and 37.0 lb.
e. Use your answers from parts (c) and (d) to construct a table of selected Type II error probabilities and powers.
f. Use your answer from part (e) to construct the power curve.
Using a sample size of 60 instead of 35, repeat
g. Part (b).
h. Part (c).
i. Part (d).
j. part (e).
k. Part (f).
l. Compare your power curves for the two sample sizes and explain the principle being illustrated.