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

Question

Daniel

Mathematics

23 August, 13:08

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

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Answers (1)

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Hadley Irwin · Answer 1

e) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken.

Step-by-step explanation:

The central limit theorem states that

"Given a population with a finite mean μ and a finite non-zero variance σ2, the sampling distribution of the mean approaches a normal distribution with a mean of μ and a variance of σ2/N as N, the sample size, increases."

This means that as the sample size increases, the sample mean of the sampling distribution of means approaches the population mean. This does not state that the sample mean will always be the same as the population mean.