Question

A department store manager believes that the average age of their customers is at least 60. To prove their point, the manager randomly selects a sample of customers and records their ages. The data is listed below. At α = 0.01, test the manager’s claim.

70 48 41 68 69 55 70 57 60 83

32 60 72 58 88 48 59 60 56 65

66 60 68 42 57 59 49 70 75 63

44

Please explain in detail. Do null and alternative hypothesis, and complete the hypothesis test.

Answer 1

There is no statistical evidence to prove that mean is atleast 60

Explanation:

Given that a department store manager believes that the average age of their customers is at least 60.

`H_0: \bar x =60\\\H_a: \bar x >60`

(Right tailed test)

significance level = 1%

Data given is

70 48 41 68 69 55 70 57 60 83

32 60 72 58 88 48 59 60 56 65

66 60 68 42 57 59 49 70 75 63

44

Mean 60.93333333

std dev 12.00268169

Std error 2.155745271

df = 30

Mean difference = 0.93

Test statistic = mean difference/std error

= 0.431405

p value = 0.3346

Since p >0.01 we accept null hypothesis

There is no statistical evidence to prove that mean is atleast 60