Q.57 - The Practice of Statistics for AP

Question

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks mote and more Normal." ls the student right? Explain your answer.

Step-by-Step Solution

Answer

The student is not right

Step-1 Given Information

Given in the question that

The statement of the student$=$As you take larger  larger samples from a population, the histogram of the sample values looks mote and more Normal.we have to find that ls the student right.

Step-2 Explanation

The central limit theorem asserts that if a population has a mean $\mu$and standard deviation $\sigma$ and large random samples with replacement are selected from the population, the sample means distribution will be approximately normal.

The student's argument is incorrect because as the sample size grows, the histogram of the sample values will take on the shape of the population distribution.

As a result, the student is incorrect.