Question

(20.30) In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 70 subjects (24 males and 46 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¯=11.73 and s=s=4.19 for the times of the 24 members of the neutral group.

(Give your answer to three decimal places.)

A 96 % confidence interval for the mean time, when using a neutral screen, in the population from which the subjects were recruited is from  to  seconds.

Answer 1

Solution :

Point estimate = sample mean = = 11.73

sample standard deviation = s = 4.19

sample size = n = 24

Degrees of freedom = df = n - 1 = 24 -1 = 23

At 96% confidence level

= 1-0.96% =1-0.96 =0.04

/2 =0.04/ 2= 0.02

t/2,df = t_{0.02,23 = 2.177}

t _/2,df = 2.177

Margin of error = E = t_/2,df * (s /n)

= 2.177 * (4.19 / 24)

Margin of error = E = 1.862

The 96% confidence interval estimate of the population mean is,

- E < <  + E

11.73 -1.862 < < 11.73 + 1.862

9.868 < < 13.592

(9.868 ,13.592)

Answer = (9.868 ,13.592)