A math teacher claims that she has developed a review course that increases the scores of students on the math portion of the SAT exam. Based on data from the College Board, SAT scores are normally distributed with µ = 515. The teacher obtains a random sample of 1800 students, puts them through the review class, and finds that the mean SAT math score of the 1800 students is 519 with a standard deviation of 111.

(a) State the null and alternative hypotheses.

(b) Test the hypothesis at the α = 0.10 level of significance. Is a mean SAT math score of 519 significantly higher than 515?

(c) Do you think that a mean SAT math score of 519 versus 515 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance?

(d) Test the hypothesis at the a = 0.10 level of significance with n = 400 students. Assume the same sample statistics.

Is a sample mean of 519 significantly more than 515? What do you conclude about the impact of large samples on the P-value ?