You may need to use the appropriate technology to answer this question. A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow. Student Math Writing 1 540 474 2 432 380 3 528 463 4 574 612 5 448 420 6 502 526 7 480 430 8 499 459 9 610 615 10 572 535 11 390 329 12 593 613 (a) Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score - writing score.) Formulate the hypotheses. OHo: Hy # 0 Ha: Hd = 0 HO: HSOO Ho: Hso Ho: Hso Ha: H = 0 O Ho: H > 0 H: H SO O Ho: Hy = 0 Ha: H # 0 Calculate the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? Do not reject Ho. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test. O Do not reject Ho. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test. O Reject Ho. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test. O Reject Ho. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test. (b) What is the point estimate of the difference between the mean scores for the two tests? (Use math score - writing score.) What are the estimates of the population mean scores for the two tests? Math Writing Which test reports the higher n