Math SAT Scores $( Y )$ Are Normally Distributed with a Mean of 500 and a a Mean

Essay

Math SAT scores $( Y )$ are normally distributed with a mean of 500 and a standard deviation of 100. 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: $H _ { 0 } : \mu _ { Y } = 500$ vs. $H _ { 1 } : \mu _ { Y } = 530$ . (a)Sketch the two distributions under the null hypothesis and the alternative hypothesis.