Determine the 95​% confidence interval for the difference in​ scores, μ1−μ2. Interpret the interval.   The lower bound is __. The upper bound is ___ ​(Round to three decimal places as​ needed.)   B Interpret the interval.

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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 23.5 with a standard deviation of 4.3​, while the 200 students in group 2 had a mean score of 17.7 with a standard deviation of 4.1.

Complete parts ​(a) and ​(b) below.

(a) Determine the 95​% confidence interval for the difference in​ scores, μ1−μ2. Interpret the interval.
 
The lower bound is __.
The upper bound is ___
​(Round to three decimal places as​ needed.)
 
B Interpret the interval. Choose the correct answer below.
 
 
A. The researchers are 95​% confident that the difference of the means is in the interval.
 
B. There is a 95​% probability that the difference of the means is in the interval.
 
C. The researchers are 95​% confident that the difference between randomly selected individuals will be in the interval.
 
D. There is a95​% probability that the difference between randomly selected individuals will be in the interval.
 
​(b) What does this say about​ priming?
 
 
A. Since the 95​% confidence interval does not contain​ zero, the results suggest that priming does have an effect on scores.
 
B. Since the 95​% confidence interval contains​ zero, the results suggest that priming does not have an effect on scores.
 
C. Since the 95​% confidence interval does not contain​ zero, the results suggest that priming does not have an effect on scores.
 
D. Since the 95​% confidence interval contains​ zero, the results suggest that priming does have an effect on scores.
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