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Statistics Problems and Hypothesis Testing

This is a question concerning the use of hypothesis testing:

A political action committee decided to poll its membership to determine if they were in favor of a certain potential law, similar to gun control. The results that came back were 125 in favor of the law, and 120 against. Given that the crew at the center would use the fact that the simple majority would win, Johnny Statman, said I don't think that is appropriate decision, and we really need to need to have our group oppose the law. How do you suppose he came up with that conclusion? What kind of analysis did he do to arrive at his decision?


Suppose you devised a training program to raise student scores on a standardized test, such as ACT, or AIMS (like in Arizona). You first administer the test to a random sample of students, record their scores, administer the training to these students, and then administer the test a second time to each of the same students. For each student you record their score for the second test. (I am deliberately leaving out additional parameters, as you will see why in item b)
a. What would the null and alternate hypothesis be?
b. Assuming there was an increase in scores, do you think that only the training method was responsible? What other factors could explain the changes?

Solution Preview

(1) Proportion of members in favor of the Law = p1 = 125/(125 + 120) = 0.56

Proportion of members against the Law = p2 = 120/(125 + 120) = 0.53

Since p1 is ...

Solution Summary

This solution is brief, but concise, providing a neat, step by step response which details how to approach these statistic based problems.