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 04 4 1 G=306 2 2 ?X2 = 138________________________________________________T = 15 T = 12 T = 3SS = 2 SS = 8 SS = 2________________________________________________a. Use these data to test whether there are any significant differences among the three age groups. Use ? = .05.SSbetween= ? T2/n – G2/N= 152/3 + 122/3 + 32/3 â 302/9=75+48+3 -100=26MSbetween=26/2=13SSwithin = 2+8+2=12MSwithin = 12/6=2F=13/2=6.5Fcritical = 5.146.5>5.14Therefore, these data are sufficient to conclude that there are significant differences among the three ages at ? = .05 b. Use the ScheffÃ© test to determine which groups are different.

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