Question: Math SAT scores ( Y ) are normally distributed with a mean of 1500 and a standard deviation of 140. An evening school advertises that

Math SAT scores (Y) are normally distributed with a mean of 1500 and a standard deviation of 140. An evening school advertises that it can improve students' scores by roughly a third of a standard deviation, or 30 points, if they attend a course which runs over several weeks. (A similar claim is made for attending a verbal SAT course.) The statistician for a consumer protection agency suspects that the courses are not effective. She views the situation as follows: H0 : = 1500 vs. H1 : = 1460.

Assume that after graduating from the course, the 420 participants take the SAT test and score an average of 1450. Is this convincing evidence that the school has fallen short of its claim at 2.5% level?

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