TESTING HYPOTHESES

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Student Number___________________

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1. Suppose public opinion polls have consistently demonstrated widespread support for increased federal spending on environmental protection. A candidate, John Tightwad, argues, however, that no more than half of the voters want more public spending in this area. The candidate's opponent doesn't believe the claim and wants to use "hard" evidence backed by "statistical theory and methods" to prove it. You're asked to consult.
1. Translate Tightwad's proposition about public opinion regarding spending for environmental protection into statistical hypotheses. You should be able to state two, one that makes a specific claim (null) and one that states an alternative.
1. _________________________________________________



2. _________________________________________________



2. There's no need to write a paragraph. Just succinctly state the two hypotheses in the manner demonstrated in the notes.



2. Your client in this undertaking doesn't have much money to spend but would still like to collect some data from voters in the district that would discredit the Tightwad's claim. So you sample 25 people and discover that 18 agree with the statement "The government in Washington should spend more money protecting the environment."
1. What sampling or probability distribution would be appropriate for this problem? ___________________
2. You can obtain it using the method presented in the notes for Class 23. Attach the distribution to this assignment.
3. Now given that the Tightwad's hypothesis is true, what is the probability of finding 18 or more people in a sample of 25 who would agree with the statement? __________________________
4. What do you tell your client, accept or reject Tightwad's claim? Why? ___________________________________________________ _________________________________________________________ _________________________________________________________________ ___________________________________________________________________________________________
3. This set of questions is based on problem 6.7 in Agresti and Finlay, Statistical Methods for the Social Sciences, page 199. The 1991 General Social Survey reports the following responses to the statement "A preschool child is likely to suffer if his or her mother works."

1. The 996 responses are "scored" 2 for strongly agree, 1 for agree, -1 for disagree, and -2 for strongly disagree. The mean response is thus -.052 with a standard deviation (s) of 1.253. The question is: are these data consistent with the hypothesis that population mean score is 0, which suggests that the public is in the middle on this question? Or is there any evidence that the public slightly disagrees with the statement and thus has what might be considered a "modern" preference regarding women's roles in society?
2. You can attack this problem systematically by stating the null and alternative hypotheses:
1. H₀: ____________________
2. H_A: ____________________
1. Make sure that the alternative is a directional hypothesis so that it reflects the nature of the problem. (In other words, the alternative should not be that the mean result does not equal some value, but that it is [pick the right one] less than or more than that value.)
3. What is the appropriate sampling distribution?_____________________

1. Sketch it in the space below or on another sheet.



































2. What "tail" of the distribution is appropriate for this test? _____________
3. You want to test the hypothesis at the .05 level. What is the critical value that defines the critical region? _________________
4. What is the standard error of the mean for this problem? _________________
5. What is the observed z?_______________________
6. Do you accept or reject the null hypothesis? Explain. ______________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________________________________________________

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