3. In the past, the average age of employees of a large corporation has been 40

Question

3. In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average are of all employees, a sample of 64 employees was selected. The average age in the sample was 45 years with a sample deviation of 16 years. Let = .05.    a. State the null and the alternative hypotheses   b. Compute the test statistic   c. Using the critical value approach, test to determine whether or not the mean age of all employees is significantly more than 40 years.

Explanation / Answer

Given n=64, xbar=45, s=16

(a) The test hypothesis is
Ho:<=40
Ha:>40

(b) The test statistic is

Z=(xbar-)/(s/n)

=(45-40)/(16/8)

= 2.5

(c) Given a=0.05, the critical value is Z(0.05)=1.645 (check standard normal table)

Since Z=2.5>1.645, we reject Ho.

So we can conclude that the mean age of all employees is significantly more than 40 years.

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