(a) Correct, because a larger sample gives more information about
the population and thus allows us to make more accurate predictions.
If the predictions are more accurate, this also means that the
variability (measured by the standard deviation) is also decreased.

(b) Correct, the standard deviation of the sampling distribution of the sample mean is the variability of the sample mean over all possible samples.

(c) Correct, the sample mean is an unbiased estimator of the population mean.

(d) Correct, because the the variation is given by the standard deviation of the sampling distribution.

(e) Incorrect, because the sampling distribution is the distribution of all possible sample means, which cannot be centered about the sample mean (since there are many sample means).

Answer: (e)

(b) Correct, the standard deviation of the sampling distribution of the sample mean is the variability of the sample mean over all possible samples.

(c) Correct, the sample mean is an unbiased estimator of the population mean.

(d) Correct, because the the variation is given by the standard deviation of the sampling distribution.

(e) Incorrect, because the sampling distribution is the distribution of all possible sample means, which cannot be centered about the sample mean (since there are many sample means).

Answer: (e)