Question

(20.30) In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 68 subjects (29 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¯= 11.5 and s= 4.31 for the times of the 24 members of the neutral group.

(Give your answer to three decimal places.)

A 90% confidence interval for the mean time in the population from which the subjects were recruited is from ___ to ____ seconds.

Answer 1

Solution :

Given that,

= 11.5

s = 4.31

n = 24

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

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,24 = 1.714

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

= 1.714 * (4.31 / 24)

= 1.508

The 90% confidence interval estimate of the population mean is,

- E < < + E

11.5 - 1.508 < < 11.5 + 1.508

9.992 < < 13.008

(9.992, 13.008 )