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 21.9 with a standard deviation of 3.4, while the 200 students in group 2 had a mean score of 19.8 with a standard deviation of 3.5.
(a) Determine the 95% confidence interval for the difference in scores μ1 - μ2.

And we are 95% confident that the true difference means are between

Step-by-step explanation:

We know the following info:

sample mean for group 1

sample mean for group 2

sample standard deviation for group 1

sample standard deviation for group 2

sample size group 1

sample size group 2

We want to find a confidence interval for the difference of means and the correct formula to do this is:

Now we just need to find the critical value. The confidence level is 0.95 then the significance is and . The degrees of freedom are given by:

The critical value for this case would be :  

And replacing into the confidence interval formula we got:

And we are 95% confident that the true difference means are between

2: 10

step-by-step explanation:

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