Answer to Question #248073 in Statistics and Probability for Sharon

Question

In the past, the average age of employees of a large corporation is more than 27 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 36 employees was selected. The average age in the sample was 30 years with a population standard deviation of 8 years. Use the 5% signification level to test the claim. (20marks)

Answer 1

$\bar{x} = 30 \\ s= 8 \\ n=36 \\ α=0.05$

Test-statistic:

$t= \frac{\bar{x} -\mu}{s / \sqrt{n}} \\ t = \frac{30 - 27 }{8 / \sqrt{36}} = 2.25$

P-value = P(t>2.25)

Degree of freedom = n-1 = 36-1=35

From t-table:

P-value = 0.15419 > 0.05

Since p-value is greater than level of significance, we can NOT reject the claim.