Sampling Distributions

Statistical Inference By,

Yaseen Ahmed Meenai

Faculty, DMS-FCS-IBA

Sampling and Sample Estimates

Sampling is the

Procedure of getting a

Sample from a Population

Sample results are ESTIMATES while Population results are PARAMETERS

For e.g. (a sample mean) is an Estimate and (a population mean) is a Parameter.

Repeated Sampling

Repeated Sampling can produce several Samples from a single population.

POPULATION

Sample1 Sample2 Sample3 ... Sample k

Mean1 Mean2 Mean3 .. Mean k

Sample Mean (Estimate) itself became a DATA

Sampling Distribution

Distribution of Sample Estimate is called a Sampling distribution

For e.g. Sampling Distribution of Mean, Sampling Distribution of Variance etc.

Class Work

Determine the Sampling Distribution of Sample Means data gathered in the last BBA-III class

Observed its SHAPE and comments.

Data Tabulation (Grouping Exercise)

Step # 01:

Finding the range

Range = Max. Min

Step # 02:

Finding the number of classes

No. of classes = 1 + 3.3 log(n)

Step # 03:

Finding the width or height (h)

h = Range/No. of classes

Class Intervals Frequency

Min ______ Min+h

Min+h ___ Min+h+h

Min+h+h _______ .

____________ Max

Mean and Variance of the Sampling Distribution of Mean

Class Intervals fi xi fi xi fi (xi-mean)2

Min ______ Min+h f1 x1 f1 x1 ..

Min+h ___ Min+h+h f2 x2 f2 x2 ..

Min+h+h _______ . f3 x3 ..

.. .. ..

____________ Max fm xm ..

f x fx fi (xi-mean)2