Neurobiologists suggest that watching tragic movies stimulates parts of the human brain in ways that may promote feelings of happiness, closeness in relationships, and a sense of community. Fran and Jill are interested in seeing how much happier people become after watching extremely sad movies.
Fran obtains a complex questionnaire about overall happiness from a research psychologist, who agrees to score the results. She then randomly selects nine people and convinces them to participate in her experiment. On the first day, the subjects fill out the questionnaire. For the next five days, they view one extremely sad movie per day. No subject watches the same movie twice and the order in which the movies are shown is randomized. On the seventh day, the subjects fill out the questionnaire again.
Fran records the difference in each person's score on the questionnaire as the score after watching sad movies for five days minus the score before watching the movies, such that a positive difference reflects an increase in overall happiness. Fran then constructs a paired confidence interval based on a t-distribution for the mean improvement in happiness score.
Fran believes that her confidence interval is valid. After showing her confidence interval to Jill, Jill asks Fran if she knows that the differences in happiness scores were normally distributed. Fran says that these differences in happiness scores had an extremely skewed distribution. Then Jill asks Fran if she knows the population standard deviation for the difference in happiness. Fran tells Jill that she does not know the population standard deviation for the differences because this type of experiment has never been conducted to her knowledge.
Which one of these would be the answers below?
A.) Fran, your paired confidence interval based on a 𝑡-distribution is not valid, because the population is not normally distributed.
B.) Fran, your paired confidence interval based on a 𝑡-distribution is not valid, because your sample was not random.
C.) Fran, your paired confidence interval based on a 𝑡-distribution is not valid, because the standard deviation of the differences in the population is not known.
D.) Fran, you should have used a two‑sample confidence interval for the difference in the mean scores of the questionnaires completed before watching the movies and after watching the movies.