Compare the test results

Question

The grade point averages of 61 students who completed a college course in financial accounting have a standard deviation of .790. The grade point averages of 17 students who dropped out of the same course have a standard deviation of .940. Do the data indicate a difference between the variances of grade point averages for students who completed a financial accounting course and students who dropped out? Use α = .05 level of significance. Use both p-value and critical value approaches. Compare the test results.

 

Answer 1

Data

N1 = 61, SD1 = 0.79, N2 = 17, SD2 = 0.94

S1² = 0.79² = 0.6241

S2² = 0.94² = 0.8836

Hypothesis Formation

H₀: σ1 = σ2

H₁: σ1 ≠ σ 2

Test Stastistics

F =S1²/S2²

Critical Region

Reject H0 in favor of alternative if F test statistic lesser than the critical value of F critical value or lesser than -F critical value.

i.e F-test statistic > critical value of F OR F-test statistic < critical value of -F

Critical value of F at 0.05 Significance Level for two tail test

Df1 = N1 - 1 = 61 - 1 = 60

Df2 = N1 - 1 = 17 - 1 = 16

Critical value of F with df 8 and alpha 0.05 = F_0.05/2,60,16 = 2.45

Computation

F-Statistic = 0.6241/0.8836

    = 0.71

Decision

As F statistic is neither greater than 2.45 nor smaller than -2.45 so we can not reject null hypothesis. P-value can't be determine in this manually however it can be said that it will be at least greater than the tolerance level of 0.05.