Question

hoose the correct definition of a sampling distribution. The sampling distribution of a statistic of size n n is the distribution of the parameter in one simple random sample of size n n from a given population. the distribution of all values of the parameter resulting from all populations of size n n. the distribution of the statistic in all possible samples of size n n from a given population. the distribution of the statistic in one simple random sample of size n n from a given population. the distribution of the values obtained from a simple random sample of size n n from the same population.

Answer 1

Correct option:

"The distribution of the statistic in all possible samples of size n from a given population."

Explanation:

The sampling distribution is a probability distribution of a sample statistic.

A sample statistic is a numerical value representing a characteristic of a sample. For example, the sample mean represents the mean value of the sample, the sample variance represent the variance of the sample. Both of these values are sample statistic.

A statistic is an unbiased estimator of the parameter value.

That is, the sample mean value can be used to estimate the value of population mean.

If various large samples are taken from a population and the sample statistic value is computed for each of these samples, then the probability distribution of theses sample statistic is known as the sampling distribution.

The mean of the sampling distribution is same as the population mean and the standard deviation of the sampling distribution is known as the standard error.

The correct option is:

"The distribution of the statistic in all possible samples of size n from a given population."