A parent interest group is looking at whether birth order affects scores on the ACT test. It was suggested that, on average, first-born children earn lower ACT scores than second-born children. After...

A parent interest group is looking at whether birth order affects scores on the ACT test. It was suggested that, on average, first-born children earn lower ACT scores than second-born children. After surveying a random sample of 100 first-born children, the parents’ group found that they had a mean score of 20.4 on the ACT. A survey of 125 second-born children resulted in a mean ACT score of 20.7. Assume that the population standard deviation for first-born children is known to be 1.6 points and the population standard deviation for second-born children is known to be 0.9 points. Is there sufficient evidence at the 2% level of significance to say that the mean ACT score of first-born children is lower than the mean ACT score of second-born children? Let first-born children be Population 1 and let second-born children be Population 2.