# Probability question - don't know how to do .?

You want to see if a redesign of the cover of a mail-order catalogue will increase the mean sales . A random sample of 900 customers are to receive the catalogue with the new cover. For planning purposes, you are willing to assume that the sales from the new catalogue will be approximately normally distributed...
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You want to see if a redesign of the cover of a mail-order catalogue will increase the mean sales . A random sample of 900 customers are to receive the catalogue with the new cover. For planning purposes, you are willing to assume that the sales from the new catalogue will be approximately normally distributed with sd = 50 dollars. The mean sales for the original catalogue is 25 dollars. You wish to test

Ho : mean = 25

Ha :mean > 25

You decide to reject Ho if the sample mean sales x > 26 and to accept Ho otherwise

(a) Find the probability of a Type I error, that is, the probability that your test rejects Ho when in fact mean = 25 dollars.

(b) Find the probability of a Type II error when mean = 28 dollars.This is the probability that your test accepts Ho when in fact mean = 28.

(c) Find the probability of a Type II error when mean = 30.

(d) 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 sales X will be approximately normal?

Ho : mean = 25

Ha :mean > 25

You decide to reject Ho if the sample mean sales x > 26 and to accept Ho otherwise

(a) Find the probability of a Type I error, that is, the probability that your test rejects Ho when in fact mean = 25 dollars.

(b) Find the probability of a Type II error when mean = 28 dollars.This is the probability that your test accepts Ho when in fact mean = 28.

(c) Find the probability of a Type II error when mean = 30.

(d) 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 sales X will be approximately normal?

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