Example 1:

Colin, a stockbroker at Critical Securities, reported that the mean rate of return on a sample of 10 software stocks was 12.6 percent with a standard deviation of 3.9 percent.  The mean rate of return on a sample of 8 utility stocks was 10.9 percent with a standard deviation of 3.5 percent.  At the .05 significance level, can Colin conclude that there is more variation in the software stocks?

Step 1: State the null and alternative Hypotheses:

Step 2: Select the level of significance:

Step 3: Identify the test statistic:

Sample size > 29 use z; Sample size < 30 For comparing 2 sample variances, use F statistic

Step 4: Formulate a Decision Rule:

Ho is rejected if F > 3.68, df=(9,7) ( ) (critical value)

Step 5: Compute the value of the test statistic:

Step 6: Decide on Ho:

Ho is not rejected because 1.2416 < 3.68

Interpretation: There is insufficient evidence to claim more variation in the software stock.