1.The central limit theorem says that:
a) Y(bar) is consistent for its mean.
b) Y has a standard normal distribution in large samples.
c) Y(bar) is converge in probability to its mean.
d) the distribution of Y is approximately normally distributed in large samples.
2. If the regression errors are homoskedastic, implies:
a) the least squares assumptions are not satisfied.
b) the OLS estimator is biased.
c) the OLS estimator is BLUE.
D) Var(X) = Var(e)
3. The result that E(a(hat)1) = a1 is important because:
a) Since a(hat)1 is a constant it will always equal a1
b) a(hat)1 is a random variable, so it has to equal a1.
c) a(hat)1 is a random variable, it can take on many different values and so if it is centered around the true a1, we can have confidence that doing hypotheis testing regarding a1 is valid.
d) We believe that a(hat)1 is true.
d) the distribution of Y is approximately normally distributed in large samples
Reason: According to central limit theorem, under general ...
This solution helps contextualize the central limit theorem.