Question

PROBLEM # 2: Aptitude test should produce scores with a large amount of variation so that an administrator can distinguish between persons with low aptitude and those with high aptitude. The standard test used by a certain industry has been producing scores with a standard deviation of 5 points. A new test is tried on 20 prospective employees and produces a sample standard deviation of 8 points. Are scores from the new test! significantly more variable than scores from the standard? Use a = 0.05 (25 pts).

Answer 1

Given that, population standard deviation (0)=5 sample size (n) = 20 sample standard deviation (s)=8 population variance (o^2)=25 sample variance (s^2) = 64 null, Ho: 0 <= 5; alternate, H1 : 0 >5 level of significance, alpha = 0.05 from standard normal table right tailed chisar^2 alpha/2 30.144 since our test is right-tailed reject Ho, if chisar^2 0 > 30.144 we use test statistic chisar^2 =(n-1)*s^2/0^2 chisar^2 cal = (20 - 1) * 64 / 25 = 19*64/25 = 48.64 critical value the value of chisar^2 alpha at los 0.05 with d.f (n-1)=19,30.144 we got chisqr^2 = 48.64 & right tailed chisar^2 alpha/2 30.144 make decision hence value of chisar^2 cal > chisar^2 alpha and here we reject Ho chisar^2 p_value =0.0002 test statistic: 48.64 critical value: 30.144 p-value:0.0002 decision: reject Ho score from the new user is significantly more variable than scores from standard