Do these exercises by hand, except the t-tests, for which you may use SPSS if you like. On the other hand, you'll need to do t-tests by hand on the final exam, so it's good to get the practice now!
Because you will not be getting any corrective feedback on this homework before the exam, you are welcome and invited to discuss it thoroughly on the web forum. If you like, you can even post candidate answers and get verification (or not!) from other people.
1. (6 pts)
(A) We flip a coin 5 times and find that it comes up heads 3 times. Test the hypothesis that the coin is fair. What assumptions have you made?
(B) Now the coin is flipped 500 times and comes up heads 300 times. Test whether the coin is fair.
(C) If we have an alternative hypothesis that the probability of heads is .6, what are the powers of the tests (for N=5 and N=500)?
2. (6 pts) Consumers of cake mixes were observed in rural and urban areas, and the frequencies with which three brands were purchased are shown below:
Duncan Hines Pillsbury Betty Crocker urban 250 200 550 rural 100 150 300Test the hypothesis that the distributions of cake mix purchases for the urban and rural consumers come from the same underlying distribution. What assumptions have you made?
3. (7 pts) A group of 500 (otherwise normal) adults viewed a recent popular film which explored the psychopathologies of serial killers (in graphic detail). After the film, half the audience was randomly assigned to a debriefing seminar, and the other half went to a control group situation (the restrooms). Measurements of blood pressure were taken immediately after the film and after the post-film treatment. Here are data from 4 subjects in each group:
seminar control before after before after 145 136 117 105 128 124 128 108 110 109 110 104 117 115 145 115(A) Test the hypothesis that the reduction is the same for both groups (using a t-test).
4. (6 pts)
(A) Test the null hypothesis that these four groups are equally probable:
group A B C D observed freq 8 6 4 2Have the conventional rules for good approximation by the continuous chi-square been satisfied?
(B) Now test the null hypothesis for these results:
group A B C D observed freq 80 60 40 20Which case (N=20 or N=200) gave the chi-square value with higher significance (i.e., smaller probability that the null hypothesis would yield a value that large or larger)?