XYZ corporation is a company that is focused on a stable workforce that has very little turnover. XYZ has been in business for 50 years and has more than 10,000 employees. The company has always promoted the idea that its employees stay with them for a very long time, and it has used the following line in its recruitment pamphlet: "The average tenure of our employees is 20 years." Since XYZ isn't quite sure if that statement is still true, a random sample of 100 employees is taken and the average age turns out to be 19 years with a standard deviation of 2 years. Can XYZ continue to make its claim, or does it need to make a change?
1. State the hypotheses.
H 0 = 20 years
H 1 ≠ 20 years
2. Determine the test statistic. Since we are testing a population mean that is normally distributed, the appropriate test statistic is:
3. Specify the significance level. Since the company would like to keep its present message to new recruits, it selects a fairly weak significance level (α = .05). Since this is a two-tailed test, half of the alpha will be assigned to each tail of the distribution. In this situation the critical values of Z = +1.96 and -1.96.
4. State the decision rule. If the computed value of Z is greater than or equal to +1.96 or less than or equal to -1.96, the null hypothesis is rejected.
5. Calculations.
Reject or fail to reject the null. Since 2.5 is greater than 1.96, the null is rejected. The mean tenure is not 20 years; therefore XYZ needs to change its statement.