In order to estimate the difference between the average yearly incomes of marketing managers in the East and West of the United States, the following information was gathered. East West n1 = 38 n2 = 42 x1 = 66 (in $1,000) X2 = 72 (in $1,000) $1 = 6 (in $1,000) $2 = 8 (in $1,000) (a) Develop an interval estimate for the difference between the average yearly incomes of the marketing managers in the East and West. Use 98% confidence. (Use East - West. Round your answers to three decimal places.) At a = 0.02, use the p-value approach and test to determine if the average yearly income of marketing managers in the East is significantly different from those in the West. (Let d = East - West.) (i) Formulate the hypotheses. O HO: H 1 - H 2 = 0 Ha : M 1 - 1 2 = 0 Ho: M 1 - 1 2 > o OH: M 1 - M2so HO : H 1 - H 2 + 0 OH2: M1 - M 2 = 0 Ho : H 1 - M 2 so OH: M 1 - M 2 = 0 Ho : M 1 - M 2 so OH: M 1 - M 2 > o (ii) What is the value of the test statistic? (Round your answer to three decimal places.) (iii) What is the p-value? (Round your answer to five decimal places.) p-value =