In a study to test the effects of science fiction movies on people's belief in the supernatural, seven people completed a measure of belief in the supernatural before and after watching a popular science fiction movie. Participants' scores are listed below with high scores indicating higher levels of belief. Using the .01 significance level, carry out a t test for dependent means to test the experimenter's assumption that the participants' belief in the supernatural would change after watching the movie.
Belief-in-Supernatural Scores
Before and After Watching Science Fiction Movie
Participant Before After
A 6 9
B 3 5
C 6 6
D 5 2
E 1 7
F 3 8
G 2 3
a. Use the five steps of hypothesis testing.
b. Sketch the distributions involved.
c. Figure the effect size and find the approximate power of this study.
d. Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample, including understanding decision errors, effect size and power, but who knows nothing about t tests of any kind (for example, you do not need to describe the steps or logic of hypothesis testing). Be sure you explain how this problem differs from a problem with a known population variance and a single sample. Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.
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