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.

Question
Sampling distributions
asked 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.

Answers (1)

2021-03-05
(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)
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Question 3 options:
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