The mean SAT score in mathematics, , is . The standard deviation of these scores is. A special preparation course claims that its graduates will score higher, on average, than the mean score. A random sample of students completed the course, and their mean SAT score in mathematics was . At the level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also .
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)
The null hypothesis:
H0:
The alternative hypothesis:
H1:
The type of test statistic:The value of the test statistic:
(Round to at least three decimal places.)
The critical value at the level of significance:
(Round to at least three decimal places.)
Can we support the preparation course's claim that its graduates score higher in SAT?YesNo