9-4 Two Variances or Standard Deviations 489 16.Blanking Out on Tests Many students have had the unpleasant experience of panicking on a test because the first question was exceptionally difficult. The arrangement of test items was studied for its effect on anxiety. The following scores are measures of “debilitating test anxiety,” which most of us call panic or blanking out (based on data from “Item Arrangement, Cognitive Entry Characteristics, Sex and Test Anxiety as Predictors of Achievement in Examination Performance,” by Klimko, Journal of Experimental Education, Vol. 52, No. 4.) Using a 0.05 significance level, test the claim that the two populations of scores have different amounts of variation. Questions Arranged from Easy to Difficult 24.64 39.29 16.32 32.83 28.02 33.31 20.60 21.13 26.69 28.90 26.43 24.23 7.10 32.86 21.06 28.89 28.71 31.73 30.02 21.96 25.49 38.81 27.85 30.29 30.72 Questions Arranged from Difficult to Easy 33.62 34.02 26.63 30.26 35.91 26.68 29.49 35.32 27.24 32.34 29.34 33.53 27.62 42.91 30.20 32.54 17.Count Five Test for Comparing Variation in Two Populations Repeat Exercise 16 “Blanking Out on Tests,” but instead of using the F test, use the following procedure for the “count five” test of equal variations (which is not as complicated as it might appear). a. For each value x in the first sample, find the absolute deviation x - x , then sort the absolute deviation values. Do the same for the second sample. b. Let c1 be the count of the number of absolute deviation values in the first sample that are greater than the largest absolute deviation value in the other sample. Also, let c2 be the count of the number of absolute deviation values in the second sample that are greater than the largest absolute deviation value in the other sample. (One of these counts will always be zero.) c. If the sample sizes are equal 1n1 = n22, use a critical value of 5. If n1 ≠ n2, calculate the critical value shown below. log1a>22 log a n1 n1 + n2b d. If c1 Ú critical value, then conclude that s 2 1 7 s 2 2. If c2 Ú critical value, then conclude that s 2 2 7 s 2 1. Otherwise, fail to reject the null hypothesis of s 2 1 = s 2 2. 18.Levene-Brown-Forsythe Test Repeat Exercise 16 “Blanking Out on Tests” using the Levene-Brown-Forsythe test. 19.Finding Lower Critical F Values For hypothesis tests that are two-tailed, the methods of Part 1 require that we need to find only the upper critical value. Let’s denote the upper critical value by FR, where the subscript indicates the critical value for the right tail. The lower critical value FL (for the left tail) can be found as follows: (1) Interchange the degrees of freedom used for finding FR, then (2) using the degrees of freedom found in Step 1, find the F value from Table A-5; (3) take the reciprocal of the F value found in Step 2, and the result is FL. Find the critical values FLand FR for Exercise 16 “Blanking Out on Tests.” 9-4 Beyond the Basics
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