Many students have had the unpleasant experience of panicking on a test because the first question was

Question:

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.

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 – x̅|, 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 second 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 first sample. (One of these counts will always be zero.)

c. If the sample sizes are equal (n₁ = n₂), use a critical value of 5. If n₁ ≠ n₂, calculate the critical value shown below.