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 x bar = 11.58 and s= 4.37 for the times of the 23 members of the neutral group.
a. Give a 95% confidence interval for the mean time in the population from which the subjects were recruited.
b. What conditions for the population and the study design are required by the procedure you used in a.? Which of these conditions are important for the validity of the procedure in this case?