Under the least squares assumptions (zero conditional mean for the error term, Xi and Yi being i.i.d., and Xi and ui having finite fourth moments), the OLS estimator for the slope and intercept
A. has an exact normal distribution for n > 15.
B. is BLUE.
C. has a normal distribution even in small samples.
D. is unbiased.
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The construction of the t-statistic for a one- and a two-sided hypothesis
A. depends on the critical value from the appropriate distribution.
B. is the same.
C. is different since the critical value must be 1.645 for the one-sided hypothesis, but 1.96 for the two-sided hypothesis (using a 5% probability for the Type I error).
D. uses ±1.96 for the two-sided test, but only +1.96 for the one-sided test.
The p-value for a one-sided left-tail test is given by
A. Pr(Z - tact ) = φ(tact).
B. Pr(Z < tact ) = φ(tact).
C. Pr(Z < tact ) < 1.645.
D. cannot be calculated, since probabilities must always be positive.
One of the following steps is not required as a step to test for the null hypothesis:
A. compute the standard error of ![]()
1.
B. test for the errors to be normally distributed.
C. compute the t-statistic.
D. compute the p-value.
Finding a small value of the p-value (e.g. less than 5%)
A. indicates evidence in favor of the null hypothesis.
B. implies that the t-statistic is less than 1.96.
C. indicates evidence in against the null hypothesis.
D. will only happen roughly one in twenty samples.
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