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

Section 9–5 Testing the Difference Between Two Variances 513Confidence Interval for the Difference Between Two Proportions1. Press STAT and move the cursor to TESTS.2. Press B (ALPHA APPS) for 2-PropZInt.3. Type in the appropriate values.4. Move the cursor to Calculate and press ENTER.ExcelStep by StepTesting the Difference Between Two ProportionsExcel does not have a procedure to test the difference between two population proportions.However, you may conduct this test using the MegaStat Add-in available on your CD. If you havenot installed this add-in, do so, following the instructions from the Chapter 1 Excel Step by Step.We will use the summary information from Example 9–9.1. From the toolbar, select Add-Ins, MegaStat>Hypothesis Tests>Compare TwoIndependent Proportions. Note: You may need to open MegaStat from theMegaStat.xls file on your computer’s hard drive.2. Under Group 1, type 12 for p and 34 for n. Under Group 2, type 17 for p and 24 for n.MegaStat automatically changes p to X unless a decimal value less than 1 is typed in for these.3. Type 0 for the Hypothesized difference and select the “not equal” Alternative, and click [OK].Hypothesis Test for Two Independent Proportionsp 1 p 2 p c0.3529 0.7083 0.5 p (as decimal)12/34 17/24 29/58 p (as fraction)12. 17. 29. X34 24 58 n0.3554 Difference0. Hypothesized difference0.1333 Standard error2.67 z0.0077 P-value (two-tailed)9–5 Testing the Difference Between Two VariancesObjective 5Test the differencebetween twovariances or standarddeviations.In addition to comparing two means, statisticians are interested in comparing twovariances or standard deviations. For example, is the variation in the temperatures for acertain month for two cities different?In another situation, a researcher may be interested in comparing the variance of thecholesterol of men with the variance of the cholesterol of women. For the comparison oftwo variances or standard deviations, an F test is used. The F test should not be confusedwith the chi-square test, which compares a single sample variance to a specific populationvariance, as shown in Chapter 8.If two independent samples are selected from two normally distributed populationsin which the variances are equal ( s 2 1 s 2 2) and if the variances s 2 1 and s 2 2 are compared2sas 1, the sampling distribution of the variances is called the F distribution.s 2 2Characteristics of the F Distribution1. The values of F cannot be negative, because variances are always positive or zero.2. The distribution is positively skewed.3. The mean value of F is approximately equal to 1.4. The F distribution is a family of curves based on the degrees of freedom of the varianceof the numerator and the degrees of freedom of the variance of the denominator.9–43