4. Understanding the sampling distribution of M Aa Aa You are interested in esti

Question

4. Understanding the sampling distribution of M Aa Aa You are interested in estimating the mean of a population. You plan to take a random sample from the population and use the sample's mean as an estimate of the population mean Assuming that the population from which you select your sample is not normal, which of the statements about M are true? Check all that apply. The expected value of M is equal to the value of the population mean. The sampling distribution of the z-score of M is normal for any sample size. You can assume that the sampling distribution of M is normally distributed for any sample size. You can only assume that the sampling distribution of M is normally distributed for sufficiently large sample sizes.

Explanation / Answer

Ans:

When the population is not normally distributed,from which samples are taken,then we can not assume the distribution of sample means is normal.

You can only assume that the sampling distribution of M is normally distributed for sufficiently large sample sizes.

(then the distribution of sample mean looks more and more normal when N gets larger.)

Expected value of M is equal to population mean,when population distribution is normal,from which samples are taken or sample sizes are sufficiently large.

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