Question

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(d) Suppose that A-10 and that Var(A)-4. Then the t-statistic for testing Ho : A-7 against Hi : β, 7 is equal to 1.5. True False (e) Suppose that Yi,i = 1, . . . ,n is an i.i.d. sample with E (Y) = μγ. The sample average Ỹn is an unbiased estimator for μΥ True False (f) An unbiased estimator is consistent. True False

Answer 1

Ans:

d)False

Test statistic:

$t=\dfrac{\hat{\beta _1}}{s.e.(\hat{\beta _1})}$

standard error of slope coefficient is not given,so test statistic can't be calculated.

e)True

The sample mean is a random variable that is an estimator of the population mean. The expected value of the sample mean is equal to the population mean µ. Therefore, the sample mean is an unbiased estimator of the population mean.

f)False

An estimator is consistent if, as the sample size increases, the estimates (produced by the estimator) "converge" to the true value of the parameter being estimated. To be slightly more precise - consistency means that, as the sample size increases, the sampling distribution of the estimator becomes increasingly concentrated at the true parameter value.

An estimator is unbiased if, on average, it hits the true parameter value. That is, the mean of the sampling distribution of the estimator is equal to the true parameter value.

The two are not equivalent: Unbiasedness is a statement about the expected value of the sampling distribution of the estimator. Consistency is a statement about "where the sampling distribution of the estimator is going" as the sample size increases.