Thanks! Which of the following statements is not true? a)The sampling distributi

Question

Thanks!

Which of the following statements is not true? a)The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. b) The standard deviation of the sampling distribution of sample mean = /vn c) The sampling distribution of sample mean is approximately normal mound-shaped and symmetric for n > 30 or n = 30. d) The mean of the sampling distribution of sample mean is always the same as that off the distribution from which the sample is taken. e) The larger the sample size, the better will be the normal approximation to the sampling distribution of sample mean None of the above

Explanation / Answer

Option a) is wrong because as per the central limit theorem, the sampling distribution of the sample mean becomes approximately normal, regardless of the distribution from which the sample is taken.

Hence,

The distribution of sample and distribution of sample means can be different.

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