Question

A shopper in a grocery store purchases 22 items on average. A store manager believes that the mean is greater than 22. She surveyed a randomly selected group of 40 customers and found that the mean of the number of items purchases was 23.2. The population standard deviation is 3.7 items. At α= 0.05, can it be concluded that the mean is greater than 22 items?

Answer 1

This hypothesis test is a right tailed test .

The null and alternative hypothesis is

H₀ : = 22

H_a : > 22

Test statistic = z

= ( - ) /    / n

= (23.2 - 22) / 3.7 / 40

= 2.051

Test statistic = 2.051

P-value = 0.0201

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that,

It can be be concluded that the mean is greater than 22 items .