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Can we support the preparation course's claim that its graduates score higher in SAT? '7 Yes T No The mean SAT score in mathematics, u, is 508. The standard deviation of these scores is 42. A special preparation course claims that its graduates will score higher, on average, than the mean score 508. A random sample of 60 students completed the course, and their mean SAT score in mathematics was 522. At the 0.01 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 42. Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.) The null hypothesis: H : p X S p The alternative hypothesis: H : The type of test statistic: (Choose one) 0=0 030 020 0*0 00 The value of the test statistic: (Round to at least three decimal places.) X ? The p-value: (Round to at least three decimal places.)