1. A researcher asks a random sample of 72 Virginia households how much they pay monthly for utilities. The sample has an average monthly cost of $83.42 with a standard deviation of $12.75. (a) (4 points) Find the 99% confidence interval for the mean monthly cost of utilities in Virginia. Interpret the result. (b) (6 points) Another sample of 49 households in Maryland has a mean monthly utility cost of $76.50, with a standard deviation of $16.03. At the 5% level of significance, test the claim that Virginia's average utility cost is more than four dollars larger than households in Maryland