Which of the following statements are true?
(A) Central limit theorem states that the sampling distribution of the mean ($\bar{x}$) approaches a normal distribution as the sample size increases.
(B) As per Central Limit Theorem, when the sample size increases, the mean ($\bar{x}$) for the data becomes closer to the mean of overall population.
(C) The shape of t-distribution does not depend on degree of freedom.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) - (A) only
$\text{(A)} \;\Rightarrow\; \text{CLT: sampling distribution of } \bar{x} \text{ tends to normal as } n \uparrow \;\Rightarrow\; \text{True}$
$\text{(B)} \;\Rightarrow\; \text{This describes Law of Large Numbers, not CLT} \;\Rightarrow\; \text{False}$
$\text{(C)} \;\Rightarrow\; \text{t-distribution depends on degrees of freedom} \;\Rightarrow\; \text{False}$
The correct statement is (A) only.