The College Board SAT college entrance exam consists of three parts: math, writing, and critical reading (The Wall Almanac, 2012). Sample data showing the math and writing scores for a sample of 12 students who took the SAT follow.

a. Use a .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. What is the p-value and what is your conclusion?
b. What is the point estimate of the difference between the mean scores for the two tests? What are the estimates of the population mean scores for the two tests? Which test reports the higher mean score?

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Student Math 540 Writing 474 380 463 612 420 526 Student Math 480 499 610 572 390 593 Writing 430 459 615 541 335 613 574 10 502 12