Question

two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. the students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a professor, while the students in group 2 were asked to think about soccer hooligans. these pretest thoughts are a form of priming. the 200 students in group 1 had a mean score of 24.7 with a standard deviation of 4, while the 200 students in group 2 had a mean score of 16.1 with a standard deviation of 3. complete parts (a) and (b) below. (a) determine the 90% confidence interval for the difference in scores, μ₁ - μ₂. interpret the interval. the lower bound is 8.018 the upper bound is 9.182 (round to three decimal places as needed.) interpret the interval. choose the correct answer below. a. the researchers are 90% confident that the difference of the means is in the interval. b. there is a 90% probability that the difference of the means is in the interval. c. the researchers are 90% confident that the difference between randomly selected individuals will be in the interval. d. there is a 90% probability that the difference between randomly selected individuals will be in the interval.

Explanation:

Confidence intervals are about the confidence in the method used to construct the interval, not about the probability of the parameter being in the interval (since the parameter is a fixed value). Option A correctly states that the researchers are 90% confident (due to the confidence level of the interval - construction method) that the difference of the means is in the interval. Option B is incorrect as it refers to probability (the parameter is fixed). Options C and D refer to difference between randomly - selected individuals, but the confidence interval is about the difference in population means (\(\mu_1-\mu_2\)), not about individual differences.

Answer:

A. The researchers are 90% confident that the difference of the means is in the interval.