The mean SAT score in mathematics is 579. The standard deviation of these scores is 36. A special preparation course claims that the mean SAT score, J, of its graduates is greater than 579. An independent researcher tests this by taking a random sample of 41 students who completed the course; the mean SAT score in mathematics for the sample was 581. Assume that the population is normally distributed. At the 0.05 level of significance, can we conclude that the population OO mean SAT score for graduates of the course is greater than 5797 Assume that the population standard deviation of the scores of course graduates is also 36. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. O P Ho : P = 579 X S P H : p > 579 (b) Determine the type of test statistic to use. Z 0=0 OSO 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) OX0 00 X (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 579? OYes ONO