Why are sampling distributions important to the study of inf

Why are sampling distributions important to the study of inferential statistics? demonstrate your understanding by providing an example distribution from an area such as business sports medicine social science or another area with which you are familiar

Solution

First I will explain the difference between descriptive statistics and inferential statistics.

Descriptive statistics is the term given to the analysis of data that helps describe, show or summarize data in a meaningful way such that, for example, patterns might emerge from the data.

Descriptive statistics do not, however, allow us to make conclusions beyond the data we have analysed or reach conclusions regarding any hypotheses we might have made. They are simply a way to describe our data.

Inferential statistics is the branch of statistics that deals with using sample data to make valid judgments about the population from which the data came.

Descriptive Statistics

Inferential Statistics

Statistical sampling is used quite often in statistics. In this process we aim to determine something about a population. Since population size is large, we form a statistical sample by selecting a subset of the population that is of a predetermined size. By studying the sample we can use inferential statistics to determine something about the population.  Closely related to the concept of a statistical sample is a sampling distribution.

  A sampling distribution occurs when we form more than one simple random sample of the same size from a given population. These samples are considered to be independent of one another. So if an individual is in one sample, then it has the same likelihood of being in the next sample that is taken.We calculate a particular statistic for each sample. This could be a sample mean, a sample variance or a sample proportion. Since a statistic depends upon the sample that we have, each sample will typically produce a different value for the statistic of interest. The range of the values that have been produced is what gives us our sampling distribution.

The advantage of sampling distribution is that we eliminate the variability that is present in statistics.The sampling distribution is a distribution of a sample statistic.

It is a model of a distribution of scores, like the population distribution, except that the scores are not raw scores.

Some of the sampling distributions are :

i) Sampling distribution for mean.

ii) Sampling distribution for median.

iii) Sampling distribution for range.

iv) Sampling distribution for variance.

v) Sampling distribution for standard deviation.etc.

For example : Draw all possible samples of size 2 without replacement from a population consisting of 3, 6, 9, 12, 15. Form the sample distribution of sample means and verify the results.

i) E(Xbar) = µ

We have in the population 3,6,9,12,15. So here N = 5 and n = 2.

Therefore, (N C n) number of possible samples.

(N C n) = (5 C 2) = 10 (Where C is used for combination)

10 sample values and sample means are,

second table will be,

µ = x / n = 45/5 = 9

E(Xbar)=Xbar * f(Xbar)=90/10=9

Therefore , E(Xbar) = µ

Xbar is an sampling distribution.