The mean SAT score in mathematics is

521

. The standard deviation of these scores is

42

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

, of its graduates is greater than

521

. 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

527

. At the

0.05

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

521

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

42

.