# Question: A math teacher claims that she has developed a review

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 ?

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