Females, on Average, Are Shorter and Weigh Less Than Males

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: $$\begin{aligned}\widehat { \text { Studentw } } = & - 229.21 - 6.36 \times \text { Female } + 5.58 \times \text { Height } , R ^ { 2 } = 0.50 , \text { SER } = 20.99 \\& ( 43.39 )\quad\quad ( 5.74 )\quad\quad\quad\quad \quad ( 0.62 )\end{aligned}$$ 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?