The mean SAT score in mathematics is554

. The standard deviation of these scores is39

. A special preparation course claims that the mean SAT score,

,of its graduates is greater than554

. An independent researcher tests this by taking a random sample of60

students who completed the course; the mean SAT score in mathematics for the sample was567

. At the0.01

level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than554

? Assume that the population standard deviation of the scores of course graduates is also39

.

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 alist of formulas.)

(a)State the null hypothesisH

0

and the alternative hypothesisH

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 thep-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 than554

?YesNo