Jason Farmer

2021-03-04

Which of the following statements about the sampling distribution of the sample mean is incorrect?

(a) The standard deviation of the sampling distribution will decrease as the sample size increases.

(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.

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

(d) The sampling distribution shows how the sample mean will vary in repeated samples.

(e) The sampling distribution shows how the sample was distributed around the sample mean.

(a) The standard deviation of the sampling distribution will decrease as the sample size increases.

(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.

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

(d) The sampling distribution shows how the sample mean will vary in repeated samples.

(e) The sampling distribution shows how the sample was distributed around the sample mean.

tafzijdeq

Skilled2021-03-05Added 92 answers

(A) This is true because a bigger sample size provides more knowledge about the population, enabling us to make predictions that are more accurate. The variability (as determined by the standard deviation) must likewise decrease if the forecasts are more accurate.

(B) It is correct; the sample mean's variability over all feasible samples is represented by the standard deviation of the sampling distribution of the sample mean.

(C) Correct, the sample mean serves as an impartial approximation of the population mean.

(D) Correct, as the variation is provided by the sampling distribution's standard deviation.

The sampling distribution, which is the distribution of all potential sample means and cannot be centered at the sample mean, makes

(E) incorrect (since there are many sample means).

nick1337

Expert2023-05-11Added 777 answers

Don Sumner

Skilled2023-06-14Added 184 answers

Vasquez

Expert2023-06-14Added 669 answers

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