Question

At a new store, a sample of sales in 36 days was selected in order to determine whether the average sales in this store is significantly different from $2000, the average sales for your original store. You believe that the he standard deviation of sales is $200. The average sales at the new store is $2100.

A. Determine whether or not the average score of the new store is significantly different from $2000. Use ?=.05.

B. Would your answer be different if ?=.005.     Explain.

C. Construct a 95% confidence interval for the population mean

Answer 1

a) The test statistic for the test here is computed as:

Now as this is a two tailed test, the p-value is computed from the standard normal tables as :

p = 2P(Z > 3) = 2*0.0013 = 0.0026

As the p-value here is 0.0026 < 0.05, therefore the test is significant here and we can reject the null hypothesis and conclude that the average sales at the new store is significantly different.

b) Now as the p-value here is also 0.0026 < 0.005, therefore the answer would be same here too. The test is significant at this level of significance also and we have sufficient evidence that the average sales are different from 2000.

c) From standard normal tables, we get:

P( -1.96 < Z < 1.96 ) = 0.95

Therefore the confidence interval here is computed as:

This is the required 95% confidence interval for the population mean here.