Question

1. You want to see if a redesign of the cover of a mail-order catalog will increase sales. A very large number of customers will receive the original catalog, and a random sample of customers will receive the one with the new cover. For planning purposes, you are willing to assume that the mean sales for the new catalog will be approximately Normal with σ = 50 dollars and that the mean sales for the original catalog will be μ = 25 dollars. You decide to use a sample size of n = 900. You wish to test

H₀: μ = 25

Ha: μ > 25

You decide to reject H₀if x > 26 and to accept H₀otherwise.

1. Find the probability of a Type I error, that is, the probability that your test rejects H₀when in fact μ = 25 dollars.
2. Find the probability of a Type II error when μ = 28 dollars. This is the probability that your test accepts H₀when in fact μ = 28
3. The distribution of sales is not Normal, because many customers buy nothing. Why is it nonetheless reasonable in this circumstance to assume that the sample mean will be approximately Normal?

Answer 1

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