Question

A store owner surveyed 25 randomly selected customers and found the ages shown​ (in years). The mean is 27.08 and the standard deviation is 11.73 The owner wants to know if the mean age of all customers is 32 years old.

11
16
28
43
49
41
33
17
35
36
15
24
15
11
35
25
34
40
41
32
22
13
34
11
16

c) What is the value of the test​ statistic?

​d) What is the​ P-value of the test​ statistic?

​e) What do you conclude at alpha α =0.05 ?

Answer 1

Solution:

The null and alternative hypothesis are

H0: = 32

H1:     32

c)

The test statistic t is

t =   = [27.08 - 32]/[11.73 /25] = -2.097

The value of the test​ statistic t = -2.097

d)

df = n -1 = 25 - 1 = 24

Two tailed test

So ,

p value = 0.0467

e)

Since p value is less than α =0.05

Therefore we REJECT THE NULL HYPOTHESIS H₀

There is sufficient evidence to reject the claim that  the mean age of all customers is 32 years old.