Assign 9 10 PLEASE SHOW ALL WORK In a randomized comparative

Assign 9 #10 PLEASE SHOW ALL WORK

In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 69 subjects (27 males and 42 females ranging in age from 17 to 25 years) into three groups. Participants were asked to solve a series of 6 anagrams. One group was presented with the anagrams on a blue screen; one group saw them on a red screen; and one group had a neutral screen. The time, in seconds, taken to solve the anagrams was recorded. The paper reporting the study gives = 11.63 and s = 4.38 for the times of the 23 members of the neutral group. Give a 95% confidence interval for the mean time in the population from which the subjects were recruited. (Round your answers to two decimal places.) You may need to use the appropriate Appendix Table to answer this question.

Solution

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    11.63          
t(alpha/2) = critical t for the confidence interval =    2.073873068          
s = sample standard deviation =    4.38          
n = sample size =    23          
df = n - 1 =    22          
Thus,              
              
Lower bound =    9.735945967          
Upper bound =    13.52405403          
              
Thus, the confidence interval is              
              
(   9.735945967   ,   13.52405403   ) [ANSWER]