A large population has mean mu and standard deviation sigma. A random sample of

Question

A large population has mean mu and standard deviation sigma. A random sample of size n will be taken from the population. The Central Limit Theorem tells us that (A) the mean of the sampling distribution of the sample mean is mu (B) the standard deviation of the sampling distribution of the sample mean is sigma/squareroot n (C) if n is large, the sampling distribution of the sample mean is approximately normal (D) since the population is large, the sampling distribution of the sample mean must be approximately normal (E) the standard deviation of the sampling distribution of the sample mean is greater than the standard deviation of the population

Explanation / Answer

A central limit theorem states that the sampling distribution of sample mean approaches a normal distribution with mean equal to the population mean and with standard deviation equal to /sqrt(n) as the sample size increases.

Using this statement, above options A,B and C are correct.

Note: If it is one choice that is required, choose "C", as it is the most convincing out of the other statements. It mentions, "if n is large" and therefore gives the criteria too.

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