Psychologists wish to evaluate the consistency of a standardized behavioral test.The test is designed to have a variance of 225.Twenty randomly sampled tests yield a variance of 240.Assuming the underlying population is normal, test whether the actual population variance of this test appears to be significantly greater than its designed variance.State the critical value (CV), test statistic (TS), and conclusion from the test.(Use α = 0.01.)
A) CV = 27.2036; TS = 20.267; fail to reject H₀
B) CV = 36.1909; TS = 18.377; fail to reject H₀
C) CV = 36.1909; TS = 20.267; fail to reject H₀
D) CV = 27.2036; TS = 17.8125; reject H₀

Question

Quizplus · Accepted Answer

The correct test for this scenario is the chi-square test for variance. The test statistic (TS) is calculated using the formula TS = (n-1)*s^2/σ^2, where n is the sample size, s^2 is the sample variance, and σ^2 is the population variance. Here, TS = (20-1)*240/225 = 20.267. The critical value (CV) for a chi-square test with df = n-1 = 19 at α = 0.01 (right-tailed test) is approximately 36.1909. Since TS < CV, we fail to reject the null hypothesis, indicating that the actual population variance does not appear to be significantly greater than its designed variance.

Psychologists Wish to Evaluate the Consistency of a Standardized Behavioral