State the Central Limit Theorem. Choose the correct answer below. 0 A. For a ran

Question

State the Central Limit Theorem. Choose the correct answer below. 0 A. For a random sample of n observations selected from a population with mean and standard deviation , when n is sufficiently large, the sampling distribution of x will be approximately a normal distribution with mean ' and standard deviation For a random sample of n observations selected from a population with m ean and standard deviation , when n is sufficiently large, the sampling distribution of x will be approximately a normal distribution with mean × = and standard deviation For a random sample of n observations selected from a population with mean and standard deviation , when n > 4, the sampling distribution of x will be exactly a normal distribution with mean ' and standard deviation - For a random sample of n observations selected from a population with mean and standard deviation , when n is sufficiently large, the sampling distribution of x will be a uniform distribution with mean ,- and standard deviation B. ° C. 0 D.

Explanation / Answer

The correct option is A

Explanation:

Sampling Distribution of x

Suppose that ¯x is the mean of a Simple Random Sample (SRS) of size n drawn from a large population with mean and standard deviation . Then
- the mean of the sampling distribution of ¯x is ¯x = ; and,
- the standard deviation of the sampling distribution of ¯x is
¯x = / n
Rule of Thumb: You can use this formula for standard deviation when the population is at least 10 times larger than the sample

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