When do children in the united states develop preference for brand name products? In a study reported, marketers showed children identical pictures of athletics shoes. One picture was labeled Nike, and one was labeled K-Mart. The children were asked to evaluate the shoes based on their appearance, quality, price, prestige, favorableness, and preference for owning. A score from 2 to -2 was recorded for each child. The following table reports the results of the study:

Age by Brand       Sample size        Sample Mean         Sample Standard Deviation

Age 8

Nike                       27                     0.89                           0.98
K-Mart                   22                     0.86                            1.07

Age 12

Nike                       39                     0.88                            1.01
K-Mart                   41                      0.09                            1.08

Age 16

Nike                       35                      0.41                           0.81
K-Mart                   33                     -0.29                           0.92

(a) Conduct a pooled-variance t test for the difference between the two means for each of the three age groups. Use a level of significance of 0.05.

(b) What assumptions are needed to conduct the tests in(a)?

(c) Write a brief summary of your findings.