Answer: The standard deviation of the sampling distribution of M is equal to the standard deviation of the population divided by the square root of the sample size.
You can assume that the sampling distribution of M is normally distributed for any sample size.
Step-by-step explanation:
- According to the central limit theorem , if we have a population with mean
and standard deviation
, then if we take a sufficiently large random samples from the population with replacement , the distribution of the sample means will be approximately normally distributed.
- When population is normally distributed , then the mean of the sampling distribution = Population mean
- Standard deviation of the sampling distribution =
, where
So, the correct statements are:
- You can assume that the sampling distribution of M is normally distributed for any sample size.
- The standard deviation of the sampling distribution of M is equal to the standard deviation of the population divided by the square root of the sample size.