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The mean SAT score in mathematics is $74. The standard deviation of these scores is 41. A special preparation course claims that the mean SAT score, I, of its graduates is greater than $74 . An independent researcher tests this by taking a random sample of 130 students who completed the course; the mean SAT score in mathematics for the sample was 580. At the 0.10 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 574? Assume that the population standard deviation of the scores of course graduates is also 41. 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 w, and the alternative hypothesis #. (b) Determine the type of test statistic to use. (Choose one) 0=0 090 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (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 574? Yes No