Question

The mean SAT score in mathematics, μ , is 574 . The standard deviation of these scores is 39 . A special preparation course claims that its graduates will score higher, on average, than the mean score 574 . A random sample of 14 students completed the course, and their mean SAT score in mathematics was 602 . Assume that the population is normally distributed. At the 0.01 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 39 . 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.)

Answer 1

H0: Null Hypothesis: 574

HA: Alternative Hypothesis: 574 (Claim)
SE = s/

= 39/

= 10.4232

Test statistic is given by:

t = (602 - 574)/10.4232

= 2.6863

= 0.01

ndf = n - 1= 14 -1= 13

from Table, critical value of t = 2.6503

Since the calculated value of t = 2.6863 is greater than critical value of t = 2.6503, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that the prepation course does what it claims that its graduates will score higher on average than the mean score 574.