Question

The marks of 5 students in Economics are 20, 24, 20, 30 and 26. Random
samples of size 2 are drawn without replacement. Calculate E(x) and
SE (x) . How far the values of E(x) and SE (x) change if samples are
drawn by “with replacement” method?

Answer 1

Answer:

A critical part of inferential statistics involves determining how far sample statistics are likely to vary from each other and from the population parameter.

The sampling distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample of size

n

.

Sampling distributions allow analytical considerations to be based on the sampling distribution of a statistic rather than on the joint probability distribution of all the individual sample values.

The sampling distribution depends on: the underlying distribution of the population, the statistic being considered, the sampling procedure employed, and the sample size used.

Key Terms

inferential statistics: A branch of mathematics that involves drawing conclusions about a population based on sample data drawn from it.

sampling distribution: The probability distribution of a given statistic based on a random sample.