Which one of the following statements is false?
A) The sampling distribution of any statistic becomes approximately normal for large sample sizes.
B) The sampling distribution of the sample mean becomes approximately normal for large sample sizes.
C) The sampling distribution of the sample mean is exactly normal if the observations are normally distributed.
D) The standard deviation of the sample mean decreases as the sample size increases.

Question

Quizplus · Accepted Answer

The false statement is A because it generalizes that the sampling distribution of any statistic becomes approximately normal for large sample sizes, which is not always true. This statement overlooks the fact that the shape of the sampling distribution depends on the underlying distribution of the data and the statistic being considered. While the Central Limit Theorem supports the idea that the sampling distribution of the sample mean becomes approximately normal for large sample sizes (regardless of the shape of the population distribution), this principle does not apply to all statistics.

Which One of the Following Statements Is False