Question

n a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 67 subjects (28 males and 39 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⎯⎯⎯=11.77 and s=4.55 for the times of the n= 25 members of the neutral group. (Give your answer to three decimal places.) A 96 % confidence interval for the mean time in the population from which the subjects were recruited is from____to_____ seconds.

Answer 1

sample mean, xbar = 11.77
sample standard deviation, s = 4.55
sample size, n = 25
degrees of freedom, df = n - 1 = 24

Given CI level is 96%, hence α = 1 - 0.96 = 0.04
α/2 = 0.04/2 = 0.02, tc = t(α/2, df) = 2.172

ME = tc * s/sqrt(n)
ME = 2.172 * 4.55/sqrt(25)
ME = 1.977

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (11.77 - 2.172 * 4.55/sqrt(25) , 11.77 + 2.172 * 4.55/sqrt(25))
CI = (9.793 , 13.747)

A 96 % confidence interval for the mean time in the population from which the subjects were recruited is from 9.793 to 13.747 seconds.