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 23.6 with a standard deviation of 4.5​, while the 200 students in group 2 had a mean score of 18.5 with a standard deviation of 4.1. 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 nothing. The upper bound is nothing. ​(Round to three decimal places as​ needed.)   Interpret the interval. Choose the correct answer below.     A. There is a 90​% probability that the difference of the means is in the interval.   B. The researchers are 90​% confident 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. ​(b) What does this say about​ priming?     A. Since the 90​% confidence interval contains​ zero, the results suggest that priming does not have an effect on scores.   B. Since the 90​% confidence interval contains​ zero, the results suggest that priming does have an effect on scores.   C. Since the 90​% confidence interval does not contain​ zero, the results suggest that priming does have an effect on scores.   D. Since the 90​% confidence interval does not contain​ zero, the results suggest that priming does not have an effect on scores.   Click to select your answer(s).

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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
23.6
with a standard deviation of
4.5​,
while the
200
students in group 2 had a mean score of
18.5
with a standard deviation of
4.1.
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
nothing.
The upper bound is
nothing.
​(Round to three decimal places as​ needed.)
 
Interpret the interval. Choose the correct answer below.
 
 
A.
There is a
90​%
probability that the difference of the means is in the interval.
 
B.
The researchers are
90​%
confident 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.
​(b) What does this say about​ priming?
 
 
A.
Since the
90​%
confidence interval contains​ zero, the results suggest that priming does not have an effect on scores.
 
B.
Since the
90​%
confidence interval contains​ zero, the results suggest that priming does have an effect on scores.
 
C.
Since the
90​%
confidence interval does not contain​ zero, the results suggest that priming does have an effect on scores.
 
D.
Since the
90​%
confidence interval does not contain​ zero, the results suggest that priming does not have an effect on scores.
 
Click to select your answer(s).
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