Adult Males Are Taller, on Average, Than Adult Females

question 59

Essay

Adult males are taller, on average, than adult females. Visiting two recent American Youth Soccer Organization (AYSO)under 12 year old (U12)soccer matches on a Saturday, you do not observe an obvious difference in the height of boys and girls of that age. You suggest to your little sister that she collect data on height and gender of children in 4^th to 6^th grade as part of her science project. The accompanying table shows her findings.
Height of Young Boys and Girls, Grades 4-6, in inches
(a)Let your null hypothesis be that there is no difference in the height of females and males at this age level. Specify the alternative hypothesis.
(b)Find the difference in height and the standard error of the difference.
(c)Generate a 95% confidence interval for the difference in height.
(d)Calculate the t-statistic for comparing the two means. Is the difference statistically significant at the 1% level? Which critical value did you use? Why would this number be smaller if you had assumed a one-sided alternative hypothesis? What is the intuition behind this?

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