You may need to use the appropriate appendix table or technology to answer this question. 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 72 = 44 x, = 75 (in $1,000) X2 = 81 (in $1,000) 51 = 7 (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.) to (b) 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. Ho: H1 - H2SO Ha: H1 - H2 = 0 HO: Hi - H250 Ha : H 1 - H 2 2 0 Ho: H1 - H2 = 0 Ha: H1 - H2 0 O' Ho: H1 - H2 > 0 Ha: H 1 - H2 so HO: Hi - H2 * 0 Ha : H 1 - H2 = 0 (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 = iv) What is your conclusion? Do not reject Ho. We can conclude that there is a significant difference between the average yearly incomes of marketing managers in the East and West. O Reject Ho. We cannot conclude that there is a significant difference between the average yearly incomes of marketing managers in the East and West. O Reject Ho. We can conclude that there is a significant difference between the average yearly incomes of marketing managers in the East and West. O Do not reject Ho. We cannot conclude that there is a significant difference between the average yearly incomes of marketing managers in the East and West