Question

In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 69 subjects (28 males and 41 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 ¯ = 11.54 and s= s = 4.35 for the times of the 25 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

sample std dev ,    s =    4.3500
Sample Size ,   n =    25
Sample Mean,    x̅ =   11.5400

Level of Significance ,    α = 1-0.96 = 0.04          
degree of freedom=   DF=n-1=   24          
't value='   tα/2=   2.1715 [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   4.350   / √   25   =   0.8700
margin of error , E=t*SE =   2.1715   *   0.870   =   1.889
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    11.54   -   1.889   =   9.6508
Interval Upper Limit = x̅ + E =    11.54   -   1.889   =   13.4292
96%   confidence interval is (   9.651 < µ <   13.429 )