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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. The statistician for a consumer protection agency suspects that the courses are not effective. She views the situation as follows: H0: μ_0 = 500 vs. H1:μ_a = 530.
a) The statistician send 49 students for the school and after graduating from the course, the 49 participants take the SAT test and score an average of 520. Is this convincing evidence that the school has fallen short of its claim? What is the p-value for such a score under the null hypothesis?
b) What would be the critical value under the null hypothesis if the size of your test were 5%?
Test hypothesis that people in State A are more depressed than U.S. population. Illustrate all of your hypothesis steps. (Use alpha = .01.)
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At the .01 level of significance, is the true mean greater than 10?
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The p-value of the test is closest to:
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The calculated Z test statistic is a positive value that leads to a p-value of .045 for the test. If the significance level (α) is .01, the null hypothesis would be rejected.
How large should the sample be if I want to maintain a 95 percent level of confidence and suffer a maximum error of $2.00 in my estimate of the highest price consumers are willing to pay?
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