The College Board SAT college entrance 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 SAT follow. Student Math Writing Student Math Writing
1 540 474 7 480 430
2 432 380 8 499 459
3 528 463 9 610 615
4 574 612 10 572 541
5 448 420 11 390 335
6 502 526 12 593 613

Required:
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. What is the test statistic?
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?