The mean SAT score in mathematics is
512
. The standard deviation of these scores is
42
. A special preparation course claims that the mean SAT score,
\mu
, of its graduates is greater than
512
. An independent researcher tests this by taking a random sample of
150
students who completed the course; the mean SAT score in mathematics for the sample was
513
. At the
0.05
level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than
512
? Assume that the population standard deviation of the scores of course graduates is also
42
.
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.â–¼(Choose one)
(c)Find the value of the test statistic. (Round to three or more decimal places.)
(d)Find the critical 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
512
?