A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20,while 16 males had a mean of $17.30 with a standard deviation of $9.60.In comparing the population variances at $\alpha$ = .10 in a two-tailed test,we conclude that:
A) the variances are equal.
B) the variances are unequal.
C) the variances are incomparable (different sample sizes).

Question

Quizplus · Accepted Answer

We need to use the F-test to compare the variances. The formula for the F-test is F = s12/s22, where s12 is the variance of the first sample and s22 is the variance of the second sample. We can calculate the F-value as F = (3.20)2/(9.60)2 = 0.111. The degrees of freedom are n1 - 1 = 15 and n2 - 1 = 15. Using an F-table with these degrees of freedom and a significance level of 0.10, we get a critical F-value of 0.435. Since our calculated F-value is less than the critical value, we fail to reject the null hypothesis that the variances are equal. Therefore, we can conclude that the variances are unequal.

A Random Sample of Ersatz University Students Revealed That 16 α\alphaα

A Random Sample of Ersatz University Students Revealed That 16 $\alpha$