Two researchers concluded a study in which two groups of students were asked to

Question

Two researchers concluded 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 22.7 with a standard deviation of 3.9, while the 200 students in group 2 had a mean score of 16.9 with a standard deviation of 2.8. Complete parts (a) and (b) below. (a) Determine the 90% confidence interval for the difference in scores. mu_1 - mu_2. Interpret the interval (___________ ___________) (Round to three decimal places as needed) interpret the interval. Choose the correct answer below There is a 90% probability that the difference of the means is in the interval The researchers are 90% confident that the difference of the means is in the interval The researchers are 90% confident that the difference between randomly selected individuals will be the interval There is a 90% probability that the difference between randomly selected individuals will be in the interval (b) What does this say about priming? Since the 90% confidence interval contains zero, the results suggest that priming does have an effect on scores. Since the 90% confidence interval contains zero, the results suggest that priming does not have an effect on scores Since the 90% confidence interval contains zero, the results suggest that priming does have an effect on scores.

Explanation / Answer

Sol:

given

n1=200

mu1=22..7

sd1=3.9

n2=200

mu2=16.9

sd2=2.8

z alpha/2 for 90%=1.645

90% confidence interval for difference in means

=diff in means+-z critsqrt(sd1^2/n1+sd2^2/n2)

=(22.7-16.9)+-1.645sqrt(3.9^2/200+2.8^2/200)

=5.8+-0.5585

=5.8-0.5585,5.8+0.5585

=5.2415,6.3585

=5.242,6.359

5.242<mu1-mu2<6.359

lower limit=5.242

upper limit=6.359

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

OPTION B

confidence intterval does not contain zero

OPTION C

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