Question:
Problem 10.67:According to the General Accounting Office of the U.S. government, the average age of a male federal worker is 43.6 years and that of a male worker in the non-federal sector is 37.3 years. Is there any difference in the variation of ages of men in the federal sector men in the nonfederal sector? Suppose a random sample of 15 male federal workers is taken and the variance of their ages is 91.5. Suppose also a random sample of 15 male nonfederal-sector workers is taken and the variance of their ages is 67.3. Use these data and alpha of .01 to answer the question. Assume ages are normally distributed.

Manual Solutions:

Step 1:
This is a two -tailed test. The null and alternative hypothesis are:

Ho:
Ha:

Step 2:
The appropriate test statistic is:

Step 3:
Alpha of .01, since test is two-tailed divide it by 2, alpha is = .005

Step 4:
The degrees of freedom are as follows:

The critical F value obtained from table A.7 is:


The decision rule is to reject the null hypothesis if the observed value of F is greater than 4.25 or less than .24.

Step 5:
The following sample variances are computed from the data:

Step 6:
The calculated F value is:

Step 7:
The calculated value of F = 1.366 is less than the upper tail critical value of 4.25, we therefore fail to reject the null hypothesis.

Step 8:
The age variance of male working in federal U.S. govt. is greater than the variance of male working in nonfederal U.S. government. For further examination, the company may get more information about this result that younger males are likely to work in nonfederal than federal U.S. governments.

The following graph shows the critical and calculated F values:

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