27. Does Score Variability Differ by Gender? Recently, researchers have been examining the evidence for whether there is greater variability in boys' scores than girls' scores on cognitive abilities tests. For example, one study found that boys were overrepresented at both the top and the bottom of nonverbal reasoning tests and quantitative reasoning tests.19 Suppose that the standard deviation for girls' scores is known to be 50 points for a particular test and that the population of all scores is normal. A random sample of 101 boys has a sample variance of 2600. Test whether the population standard deviation for boys exceeds 50 points, using level of significance .
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method: . Reject if . . . . Since is not , we do not reject . There is insufficient evidence that the population standard deviation of test scores for boys is greater than 50 points.
Critical-value method: . . Reject if . Since is not , we do not reject . There is insufficient evidence that the population standard deviation of test scores for boys is greater than 50 points.