1. (7 points) 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 statistics for the two periods. Assume the population standard deviation of 5.8 minutes for 1981 levels and 4.3 minutes for 2008 levels. Sample Size Sample Mean Population Standard (minutes) Deviation 1981 Levels 1 = 30 & = 30 01 = 5.8 2008 Levels n2 = 30 X2 = 24 72 = 4.3 a. Compute the standard error of X1 - X2. b. Compute the margin of error for a 95% confidence interval for the difference between two population mean times on household chores. C. Construct a 95% confidence interval for the difference between two population mean times on household chores. d. Conduct a test based on the study's claim that children today spend less time on household chores as compared to children in 1981. At the 5% significance level, do the data support the study's claim? Use the critical value approach. e. Repeat the hypothesis test in part c using the p-value approach