The mean SAT score in mathematics is 561. The standard deviation of these scores is 49. A special preparation course claims that the mean SAT score, , of its graduates is greater than 561. An independent researcher tests this by taking a random sample of 34 students who completed the course; the mean SAT score in mathematics for the sample was 564. Assume that the population is normally distributed. At the 0.10 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 561? Assume that the population standard deviation of the scores of course graduates is also 49. 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 H0 and the alternative hypothesis H1. H0: H1:

(b) Determine the type of test statistic to use. (Choose one: Z,t, Chi-square, f)

Degrees of freedom:

(c) Find the value of the test statistic. (Round to three or more decimal places.)

(d) Find the p-value. (Round to three or more decimal places.)

(e) Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 561? Yes or No