The mean SAT score in mathematics is 528. The standard deviation of these scores is 48. A special preparation course claims that the mean SAT score, μ, of its graduates is greater than 528. An independent researcher tests this by taking a random sample of 90 students who completed the course; the mean SAT score in mathematics for the sample was 532. At the 0.01 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 528? Assume that the population standard deviation of the scores of course graduates is also 48. 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 H₁ and the alternative hypothesis H₁. (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) □ P |x X 10 0=0 □口 O S 0 OSO O0

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