A new study has found that, on average, 6- to 12-year-old children are spending less time on daily household chores today compared to 1981 levels (The Wall Street Journal, August 27, 2008). Suppose two samples representative of the study’s results report the following summary statistics for the two periods:

1981 Levels2008 Levels

x̅1 = 30 minutes........
2 = 24 minutes

s1 = 4.2 minutes........ s2 = 3.9 minutes

n1 = 30..........n2 = 30

a. Specify the competing hypotheses to test the study’s claim that children today spend less time on household chores as compared to children in 1981.

b. Calculate the value of the test statistic assuming that the unknown population variances are equal.

c. Approximate the p-value.

d. At the 5% significance level, do the data support the study’s claim? Explain.

e. Repeat the hypothesis test using the critical value approach.