Question

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5.26 What is wrong? Explain what is wrong in each of the following statements. (a) The central limit theorem states that for large n, the population mean u is approximately Normal. (b) For large n, the distribution of observed values will be approximately Normal. (c) For sufficiently large n, the 68–95–99.7 rule says that I should be within u + 20 about 95% of the time. (d) As long as the sample size n is less than half the population size N, the standard deviation of x is o n

Answer 1

a) The Central limit theorem states that for large n, the sampling distribution of $\bar x$ is approximately Normal.

b) For large n, the distribution of sample mean will be approximately Normal.

c) For sufficiently large n, the 68-95-99.7 rule says that about 95% of the observations fall within $\mu \pm 2\sigma$.