CUET Preparation Today
Which of the following is not correct about the Central Limit Theorem? |
The sampling distribution of the sample mean approaches a bell-shaped curve as the sample size gets larger. A sample size of 30 or more is considered to be sufficient to hold the Central Limit Theorem. As the sample size becomes larger, the prediction of characteristics of the population becomes more accurate. The sampling distribution of the sample mean approaches a Poisson distribution as the sample size gets larger. |
The sampling distribution of the sample mean approaches a Poisson distribution as the sample size gets larger. |
The correct answer is Option (4) → The sampling distribution of the sample mean approaches a Poisson distribution as the sample size gets larger. $\text{Central Limit Theorem (CLT) states:}$ $\text{1. The sampling distribution of the sample mean approaches a normal (bell-shaped) distribution as the sample size increases.}$ $\text{2. A sample size of 30 or more is generally considered sufficient for the CLT to hold.}$ $\text{3. Larger sample sizes make estimates of population characteristics more accurate.}$ $\text{4. The sampling distribution does not approach a Poisson distribution; it approaches a normal distribution.}$ $\text{The incorrect statement is: “The sampling distribution of the sample mean approaches a Poisson distribution as the sample size gets larger.”}$ |
