The mean SAT score in mathematics is 574 . The standard deviation of these scores is 27 . A special preparation course c

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The mean SAT score in mathematics is
574
. The standard deviation of these scores is
27
. A special preparation course claims that the mean SATscore,
μ
, of its graduates is greater than
574
. An independent researcher tests this by taking a randomsample of
39
students who completed the course; the mean SATscore in mathematics for the sample was
578
. Assume that the population is normallydistributed. At the
0.10
level of significance, can we conclude thatthe population mean SAT score for graduates of the courseis greater than
574
? Assume that the population standard deviation of thescores of course graduates is also
27
.
Perform a one-tailed test. Then complete the partsbelow.
Carry your intermediate computations to three or more decimalplaces, and round your responses as specified below. (If necessary,consult a l