The mean SAT score in mathematics is $54. The standard deviation of these scores is 39. A special preparation course claims that the mean SAT score, J, graduates is greater than 354. An independent researcher tests this by taking a random sample of 60 students who completed the course; the mean SAT in mathematics for the sample was 567. At the 0.01 level of significance, can we conclude that the population mean SAT score for graduates of the course greater than 354? 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 formul (a) State the null hypothesis Ho and the alternative hypothesis H,. H P Ho : 1 X S H : 1 (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00