sample x1=2, x2=3, x4=5 from iid Uniform(1,b). Find the maximum likelihood estimation of b

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Heteroskedasticity arises because of non-constant variance of the error terms. We said proportional heteroskedasticity exists when the error variance takes the following structure: Var(et)=σt^2=σ^2 xt. But as we know, that is only one of many forms of heteroskedasticity. To get rid of that specific form of heteroskedasticity using Generalized Least Squares, we employed a specific correction – we divided by the square root of our independent variable x. And the reason why that specific correction worked, and yielded a variance of our GLS estimates that was sigma-squared, was because of the following math: (Picture 1) Where var(et)=σ^2  according to our LS assumptions. In other words, dividing everything by the square root of x made this correction work to give us sigma squared at the end of the expression. But if we have a different form of heteroskedasticity (i.e. a difference variance structure), we have to do a different correction to get rid of it. (a) what correction would you use…

Women athletes at the University of Colorado, Boulder, have a long-term graduation rate of 67%.  Over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated.  Does this indicate that the population proportion of women athletes who graduate from the University of Colorado, Boulder, is now less than 67%? Use α = 0.05 level of significance to test.