Question

Score: 0 of 1 pt 31 of 43 (26 complete) V Score: 36.85%, 15...- 11.3.11 Question Help 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 22.9 with a standard deviation of 3.8, while the 200 students in group 2 had a mean score of 18.3 with a standard deviation of 3.8. Complete parts (a) and (b) below. (a) Determine the 95% confidence interval for the difference in scores, H1-12. Interpret the interval. The lower bound is The upper bound is (Round to three decimal places as needed.)

Answer 1

Sample Size Sample mean Sample S.D ni = 200 X1 = 22.9 S1 = 3.8 Sample 1 Sample 2 n2 =200 X2 = 18.3 S2 = 3.8 2 Si 2 S2 Standard Error = + = sqrt[(3.82/200)+(3.82/200)] = 0.38 ni n2 2 si ni + sz n2 Degrees of freedom = 2 1 1 Sí ni + sz n2 n1 - n2 =[(3.8²/200)+(3.82/200)]°/[(1/(200-1))*(3.82/200)2+(1/(200-1))*(3.8²/200)?] = 398 398 Confidence Level = 95 Significance Level = a = (100-95)% = 0.05 Critical value = t* = 1.966 [using Excel =TINV(0.05,398)] Margin of Error = t*(standard error )= 1.966*0.38 = 0.7471 Lower Limit = (X7-X2 )- Margin of Error = (22.9 - 18.3) - 0.7471 = 3.853 Upper Limit = (X1-22 )+ Margin of Error = (22.9 - 18.3) + 0.7471 = 5.347