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

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 24.1 with a standard deviation of 4.6, while the 200 students in group 2 had a mean score of 17.6 with a standard deviation of 4. Complete parts (a) and (b) below (a) Determine the 90% confidence interval for the difference in scores, ??-u2 Interpret the interval. The lower bound is The upper bound is (Round to three decimal places as needed.)

Explanation / Answer

Solution :
Given that n1 = 200 , x1 = 24.1 , s1 = 4.6
n2 = 200 , x2 = 17.6 , s2 = 4

For 90% confidence interval , t = 1.65

The 90% confidence interval for the difference means is (x1 - x2) +/- t*sqrt((s1^2/n1^2) + (s2^2/n2^2))

=> (24.1 - 17.6) +/- 1.65* sqrt((4.6^2/200^2) + (4^2/200^2))

=> 6.450 , 6.550
=> The lower bound is 6.450
=> The upper bound is 6.550

  

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