In: Statistics and Probability
3. Are you smarter than your older brother? A study of birth order and intelligence, IQ tests were given to 18 and 19 year old men to estimate the size of the difference, if any, between the mean IQs of first born and second born sons. The following date for 10 first born sons and 10 second born sons are consistent with means and standard deviations reported in this article. It is reasonable to assume that the samples come from populations that are approximately normal. Second Born 103 103 91 113 102 103 92 90 114 113 First Born 104 82 102 96 129 89 114 107 89 103
a. Construct a 95 % confidence interval for the difference in Mean IQ between firstborn and second born sons?
b. Can you conclude that there is difference in mean IQ between firstborn and second born sons? Use the α=0.01 level of significance.