Question

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to have a level of significance at 0.01, what decision should she make?

A) Reject H0.

B) Do not reject H0.

C) We cannot tell what her decision should be from the information given.

D) Reject H1.

Answer 1

Solution:

For the given scenario, we have to use one sample t test for population mean.

H₀: µ = 30 versus H_a: µ > 30

This is an upper tailed test.

We are given

Level of significance = α = 0.01

Xbar = 30.45

S = 5

n = 250

df = n – 1 = 249

Upper critical value = 2.3414

(by using t-table)

Test statistic formula is given as below:

t = (Xbar - µ) / [S/sqrt(n)]

t = (30.45 – 30)/[5/sqrt(250)]

t = 1.4230

P-value = 0.0780

(by using t-table)

P-value > α = 0.01

So, we do not reject the null hypothesis

B) Do not reject H0.