The mean SAT score in mathematics, u, is 565. The standard deviation of these scores is 32. A special preparation course claims that its graduates will score higher, on average, than the mean score 565. A random sample of 44 students completed the course, and their mean SAT score in mathematics was 574. Assume that the population is normally distributed. 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 32. 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.) H, :0 The null hypothesis: The alternative hypothesis: H : = OSO The type of test statistic: (Choose one) = O O The value of the test statistic: (Round to at least three decimal places.) The critical value at the 0.01 level of significance: (Round to at least three decimal places.) Can we support the preparation course's claim that itc graduates score higher in SAT? Yes No