Question

In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 68 subjects (26 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¯= 11.51 and s= 4.25 for the times of the n= 21 members of the neutral group. (Give your answer to three decimal places.) A 95 % confidence interval for the mean time in the population from which the subjects were recruited is from to seconds.

Answer 1

Solution :

Given that,

= 11.51

s = 4.25

n = 21

Degrees of freedom = df = n - 1 = 21 - 1 = 20

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,20=2.086

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

= 2.086 * (4.25 / 21)

= 1.934

Margin of error =1.934

The 95% confidence interval estimate of the population mean is,

- E < < + E

11.51 - 1.934 < < 11.51 + 1.934

9.575 < < 13.445

(9.575 , 13.445 )