Bluman A.G. Elementary Statistics- A Step By Step Approach

516 Chapter 9 Testing the Difference Between Two Means, Two Proportions, and Two VariancesWhen you are testing the equality of two variances, these hypotheses are used:Right-tailed Left-tailed Two-tailedH 0 : s 2H 1 : s 2 1 s 2 21 s 2 2H 0 : s 2H 1 : s 2 1 s 2 21 s 2 2H 0 : s 2H 1 : s 2 1 s 21 s 2 22There are four key points to keep in mind when you are using the F test.Unusual StatOf all U.S. births, 2%are twins.Notes for the Use of the F Test1. The larger variance should always be placed in the numerator of the formula regardless ofthe subscripts. (See note on page 519.)F s2 1s 2 22. For a two-tailed test, the a value must be divided by 2 and the critical value placed on theright side of the F curve.3. If the standard deviations instead of the variances are given in the problem, they must besquared for the formula for the F test.4. When the degrees of freedom cannot be found in Table H, the closest value on the smallerside should be used.Assumptions for Testing the Difference Between Two Variances1. The samples must be random samples.2. The populations from which the samples were obtained must be normally distributed.(Note: The test should not be used when the distributions depart from normality.)3. The samples must be independent of one another.Remember also that in tests of hypotheses using the traditional method, these fivesteps should be taken:Step 1Step 2Step 3Step 4Step 5State the hypotheses and identify the claim.Find the critical value.Compute the test value.Make the decision.Summarize the results.Example 9–14Heart Rates of SmokersA medical researcher wishes to see whether the variance of the heart rates (in beats perminute) of smokers is different from the variance of heart rates of people who do notsmoke. Two samples are selected, and the data are as shown. Using a 0.05, is thereenough evidence to support the claim?Smokersn 1 26s 2 1 36Nonsmokersn 2 18s 2 2 109–46