The sampling distribution is a probability distribution that shows all possible

Question

The sampling distribution is a probability distribution that shows all possible values that a particular statistic, computed using a particular sample size from a particular population, can take on. a. What are two desirable properties of a sampling distribution? b. Why are these desirable? c. What is the way to reduce the variance of a sampling distribution when you plan to take a sample from a specific population? d. What does the Central Limit Theorem have to do with the sampling distribution?

Explanation / Answer

(1) Desirable properties of sampling distribution?

(a) Sample must be random. No biased ness should be there for any sample. A random sampling is must for having good interpretation of population from sample.

(b) Minimum variance or say efficiency. The data must have less variance doesn't contain too many outliers.

(2) These are desirable because we are interpret result of sampling distribution to calculate parameters of population. An population contain all type of data and assimilate all kind of data but a sample is just a part of it so these two property if doesn't hold true the results will show different properties of population.

(3) We can reduce the variance of sampling distribution, by increasing sample size. More the sample size the variance will be reduced.

(4) The Central limit theorem is attached to sampling distribution. As number of sample size increases, the sampling distribution of any probability distribution tend to behave like a normal distribution with estimate mean of sample equal to population mean.

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