Statistics Problems with Detailed Solution

2. A developmental psychologist is examining problem-solving ability for grade school children. Random samples of 5-year-old, 6-year-old, and 7-year-old children are obtained with n =three in each sample. Each child is given a standardized problem-solving task, and the psychologist records the number of errors. The data are as follows:
________________________________________________
___5-year-olds________6-year-olds______7-year-olds____
5 6 0
4 4 1 G=30
6 2 2 ΣX2 = 138
________________________________________________
T = 15 T = 12 T = 3
SS = 2 SS = 8 SS = 2
________________________________________________

a. Use these data to test whether there are any significant differences among the three age groups. Use α = .05.

SSbetween=  T2/n - G2/N
= 152/3 + 122/3 + 32/3 – 302/9
=75+48+3 -100
=26

MSbetween=26/2=13
SSwithin = 2+8+2=12
MSwithin = 12/6=2
F=13/2=6.5
Fcritical = 5.14
6.5>5.14

Therefore, these data are sufficient to conclude that there are significant differences among the three ages at α = .05

b. Use the Scheffé test to determine which groups are different.