The Scholastic Aptitude Test {SAT) contains three areas: critical reading, mathematics, and writing. Each area is scored on an 800-point scale. A sample of SAT scores for six students follows. student | Critical | yovhematics Writing 1 528 534 528 2 592 590 588 3 455 454 445 4 561 566 553 5 436 478 430 6 430 458 420 (a) Using a 0.05 level of significance, do students perform differently on the three areas of the SAT? State the null and alternative hypotheses. '0 FRazding ~ Hmathamatics riting H,: Not all the population means are equal. O H.: H y Hpeading MMathematics 2 Hreading = HMathematics ~ Hwriting Reading ~ \"Mathematics Heading * HMathematics * Pwriting Hg: At least two of the population means are equal. H_: At least two of the papulation means are different. Hg: Not all the population means are equal. H 2 Haeading = Hmsthematics ~ Hurriting Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Reject H,. There is sufficient evidence to conclude that the mean scores for the three parts of the SAT are not all equal. Do not reject H,. There is sufficient evidence to conclude that the mean scores for the three parts of the SAT are not all equal. Reject H. There is not sufficient evidence to conclude that the mean scores for the three parts of the SAT are not all equal. ) Do not reject H_. There is not sufficient evidence to conclude that the mean scores for the three parts of the SAT are not all equal. {b) Which area of the test seems to give the students the most trouble? Explain. The mean test scores for the three sections are for critical reading, for mathematics, and for writing. Because the [Select section has the lowest average score, this section appears to give the students the most trouble