CUET Preparation Today
Which of the following is NOT correct about the Central Limit Theorem? |
When the sample size increases, the mean of the sample of data becomes close to the mean of the overall population. When the sample size increases, the sampling distribution of the mean approaches a normal distribution, regardless of the shape of the parent population. A sample size of less than 30 is considered to be sufficient to hold the Central Limit Theorem. A sample size of 30 or more is considered to be sufficient to hold the Central Limit Theorem. |
A sample size of less than 30 is considered to be sufficient to hold the Central Limit Theorem. |
The correct answer is Option (3) → A sample size of less than 30 is considered to be sufficient to hold the Central Limit Theorem. Central Limit Theorem requires a sufficiently large sample size so that the sampling distribution of the mean becomes approximately normal. Check the statements Statement 1 is correct because with larger samples, the sample mean approaches the population mean. Statement 2 is correct because the theorem states that the sampling distribution of the mean tends to normal irrespective of the parent population shape. Statement 3 says a sample size less than 30 is sufficient. This is incorrect because small samples do not guarantee normality of the sampling distribution. Statement 4 says a sample size 30 or more is sufficient. This is correct as 30 is generally taken as the minimum size for CLT to hold. The NOT correct statement is the third one. |
