The mean SAT score in mathematics is $18. The standard deviation of these scores is 39. A special preparation course claims that the mean SAT score, u, of its graduates is greater than $18. An independent researcher tests this by taking a random sample of 80 students who completed the course; the mean SAT score in mathematics for the sample was $20. At the 0.05 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 518? Assume that the population standard deviation of the scores of course graduates is also 39. 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 Ho and the alternative hypothesis H. O P H : 0 X S p H :0 (b) Determine the type of test statistic to use. Degrees of freedom: 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) *0 00 X (d) Find the critical value. (Round to three or more decimal places.) (e) Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 518? OYes ONO