Question

QUESTION 1:

In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 68 subjects (24 males and 44 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¯¯¯=x¯=11.46 and s=s=4.18 for the times of the 26 members of the neutral group.

(Give your answer to three decimal places.)

A 98% confidence interval for the mean time in the population from which the subjects were recruited is from  to  seconds.

Answer 1

Given, x¯=11.46 and s=4.18

Standard error of mean, SE = s / = 4.18 / = 0.8198

Degree of freedom = n - 1 = 26 - 1 = 25

Critical value of t for df = 25 and 98% confidence interval is  2.485

Margin of error = t * SE = 2.485 * 0.8198 = 2.0372

98% confidence interval for the mean time is,

(11.46 - 2.0372, 11.46 + 2.0372)

(9.4228,  13.4972)

A 98% confidence interval for the mean time in the population from which the subjects were recruited is from  9.423 to 13.497 seconds.