### Assume that the null hypothesis is right

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Mr. Jones knows that over many years the mean Math SAT score of students who graduate from Irvine Remedial High School is 300, and the distribution is approximately normal, and the standard deviation is wellknown to be 100. He picks 16 students at random and gives them a weekly math review session for six months before they take the SAT. His sample of 16 students average 375 on the Math SAT. Conduct the usual hypothesis test. b) State the null hypothesis that would be used in this case. c) Assume that the null hypothesis is right. The distribution of scores in the population would then be _____ in shape, with a mean of ___ and a standard deviation which is ____ . d) The sampling distribution of X¯ will be ______ in shape, with a mean of ____ and a standard deviation of ______. e) What was X¯ for Mr. Jones' sample? f) What was the chance error of X¯ for Mr. Jones'? g) What is the "standardized sample mean" or "obtained z" value? h) "p" is the probability of getting a sample mean SAT as high as 375 just by chance. Estimate the value of p. i) Why do we use the z distribution in this case? j) Can Mr. Jones reject the null hypothesis at the .01 significance level?

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