Females, on Average, Are Shorter and Weigh Less Than Males $\widehat { \text { Studentw } }$

Essay

Females, on average, are shorter and weigh less than males. One of your friends, who is a pre-med student, tells you that in addition, females will weigh less for a given height. To test this hypothesis, you collect height and weight of 29 female and 81 male students at your university. A regression of the weight on a constant, height, and a binary variable, which takes a value of one for females and is zero otherwise, yields the following result: $\widehat { \text { Studentw } }$ = -229.21 - 6.36 × Female + 5.58 × Height, R²=0.50, SER = 20.99 (43.39)(5.74)(0.62)
where Studentw is weight measured in pounds and Height is measured in inches (heteroskedasticity-robust standard errors in parentheses).
Calculate t-statistics and carry out the hypothesis test that females weigh the same as males, on average, for a given height, using a 10% significance level. What is the alternative hypothesis? What is the p-value? What critical value did you use?