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 α = .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 can use the F-test to compare the variances of two populations. The null hypothesis is that the variances are equal, and the alternative hypothesis is that they are unequal. We can calculate the F-statistic by dividing the larger sample variance by the smaller sample variance. In this case, we have:

F = 9.6^2 / 3.2^2 = 90

The degrees of freedom for the numerator and denominator are 15 and 15, respectively. We can look up the critical values for α = .10 in a table of F-distributions or use a calculator to find that the critical values are 0.476 and 2.647. Since our calculated F-statistic (90) is greater than the critical value of 2.647, we reject the null hypothesis and conclude that the variances are unequal.

A Random Sample of Ersatz University Students Revealed That 16