Question 1 9 pts In the 2022 Whoville marble study, a simple random sample of 235 East Whoville households and an independent simple random sample of 217 West Whoville households were surveyed. Among other data, the number of kgs of marbles/household were recorded, and it was found that the sample mean weight of marbles per household in the East Whoville sample was x = 17.3 kgs, with a standard deviation of sx = 3.27 kgs, and the sample mean weight of marbles per household in the West Whoville sample was y = 18.5 kgs, with a standard deviation of sy = 4.11 kgs. (a) (2 pts) Construct a 95%-confidence interval for the mean weight of marbles per household in West Whoville. (b) (2 pts) Construct a 99%-confidence interval for the mean weight of marbles per household in East Whoville. (c) (5 pts) Test the claim at the 5% significance level that West Whoville households own more marbles (by weight) on average than East Whoville households. Include formal hypotheses, your decision and conclusion, and show how you calculate the value of the test statistic and the p-value of the test. For full (or any) credit, show your work