Paula has observed values on four independent random variables with common density f, (x) = c(, )(x

Paula has observed values on four independent random variables with common density fα,β (x) = c(α, β)(αx − β)2 exp[−(αx − β)2], where

α > 0, −∞ <β< ∞, and c(α, β) is chosen so that ∞

−∞ fα,β (x)dx = 1. She estimates α, β by maximum likelihood and computes the standard errors from the observed information. Before doing the t-test to see whether β is significantly different from 0, she consults a statistician, who tells her to use the bootstrap because observed information is only useful with large samples. What is your advice? (See discussion question 7.15.)