It is claimed that 10 year old boys and girls both have the same average height (52 inches). a researcher studies 65 boys and finds that their average height is 50.8 with a variance of 98. the 111 girls in the study had an average height of 54.1 with a variance of 123. construct a 95% confidence interval for the difference in the heights of 10 year old boys and girls based on these samples. does the confidence interval support the claim that 10 year old boys and girls have the same average height?