Which of the following statements is NOT true for sampling distributions? Provid

Question

Which of the following statements is NOT true for sampling distributions? Provide brief explanation why selected answer is Not true.

a.) An accurate sampling distribution for the mean statistic can always be identified based on a single sample without regard for sample size or knowledge of the population sampled.

b.) A sampling distribution is necessary for making confidence statements about an unknown population parameter.

c.) Depending on the population, it may not be possible to express the sampling distribution for a statistic in closed form mathematically.

d.) A sampling distribution depends on the nature of the population being sampled.

Explanation / Answer

Which of the following statements is NOT true for sampling distributions? Provide brief explanation why selected answer is Not true.

a.) An accurate sampling distribution for the mean statistic can always be identified based on a single sample without regard for sample size or knowledge of the population sampled.

This statement is false. Sample size is definitely necessary for estimating mean statistic. In general, the greater the sample size, smaller is the standard error and the estimation is more accurate.

E.g : x' = +/- z/n.

b.) A sampling distribution is necessary for making confidence statements about an unknown population parameter.

This statement is true.

c.) Depending on the population, it may not be possible to express the sampling distribution for a statistic in closed form mathematically.

This statement is true.

d.) A sampling distribution depends on the nature of the population being sampled.

This statement is true.

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