The mean SAT score in mathematics is 548. The standard deviation of these scores is 27. A special preparation course claims that the mean SAT score, ยต, of its
graduates is greater than 548. An independent researcher tests this by taking a random sample of 60 students who completed the course; the mean SAT score
in mathematics for the sample was 558. At the 0.10 level of significance, can we conclude that the population mean SAT score for graduates of the course is
greater than 548? Assume that the population standard deviation of the scores of course graduates is also 27.
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 $H_0$, and the alternative hypothesis $H_1$.
$H_0$:
$H_1$:
(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.)
(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 548?
Yes No
