Final answer:
To test the claim that the variance of homework times is less than the variance of television viewing times, we can use a hypothesis test. The null hypothesis is that the variance of homework times is greater than or equal to the variance of television viewing times, while the alternative hypothesis is that the variance of homework times is less than the variance of television viewing times.
Step-by-step explanation:
To test the claim that the variance of homework times is less than the variance of television viewing times, we can use a hypothesis test. The null hypothesis, denoted as H0, is that the variance of homework times is greater than or equal to the variance of television viewing times. The alternative hypothesis, denoted as Ha, is that the variance of homework times is less than the variance of television viewing times.
To perform the hypothesis test, we can use an F-test. We calculate the test statistic, F, which follows an F-distribution with degrees of freedom (df1 = sample size of homework times - 1) and (df2 = sample size of television viewing times - 1). We then compare the calculated F-value with the critical F-value from the F-distribution table.
If the calculated F-value is less than the critical F-value, we reject the null hypothesis and conclude that there is enough evidence to support the claim that the variance of homework times is less than the variance of television viewing times. If the calculated F-value is greater than the critical F-value, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.