Question

The Central Limit Theorem tells us three very important characteristics of the sampling distribution of the mean. Which of the following statements are NOT one of these characteristics?

1) The typical value of the sample mean
2) The amount of dispersion of the sample means
3) The shape of the sampling distribution of the mean
4) The confidence interval that contains the population mean

Answer 1

Statement 4) 'The confidence interval that contains the population mean' is not one of the characteristics described by the Central Limit Theorem (CLT). The CLT indicates that the sampling distribution will be normal, the mean equal to the population mean, and the dispersion measured by the standard error.

Step-by-step explanation:

The question is asking which statement is not one of the characteristics described by the Central Limit Theorem (CLT). The Central Limit Theorem states that if samples of sufficient size are drawn from a population, the sampling distribution of the sample mean will be normal, even if the distribution of the population is not normal. It highlights three main characteristics:

1. The distribution of the sample means will tend to be normal regardless of the shape of the population distribution.
2. The mean of the distribution of the sample means will be equal to the population mean.
3. The standard error of the mean, which measures the dispersion of the sample means, is the population standard deviation divided by the square root of the sample size (n).

Given these points, statement 4) 'The confidence interval that contains the population mean' is not a characteristic directly stated by the CLT. The CLT itself does not provide a specific confidence interval, but it does allow us to use the normal distribution to construct confidence intervals for the population mean based on sample data.