Session 1- Sampling Distribution

8/9/2019 Session 1- Sampling Distribution

1/15

Presented by Dr Sarmistha Das


2/15

` The annual earnings of the employees of a cementfactory is normally distributed with mean of Rs

25,000and SD of Rs 3000. if the HR manager draws arandom sample of size 50, what is the probabilitythat their average earnings will be more thanRs26,000?

` In a Big bazaar, the mean expenditure per customeris Rs 1850 with a SD of Rs 750. If a random sample of100 customers is selected, what is the probability thatthe, sample average expenditure per customer forthis sample is more than Rs 2000.

` Out of total production of razor blades in a day, 15%are found defective. What is the probability ofrandomly selecting 90 razor blades and finding 10 orless defective.


3/15

` By the year 2014-15, the telephone instrumentindustry is estimated to grow by 106.2 millions

units as compared to 1993-94 when the totalmarket size was only 3 million units. BhartiTeletech, BPL Telecom, Tata Telecom are some ofthe major players in the market. Bharti Teletechhas a market share of 24%. If 200 purchasers oftelephone instruments are randomly selected,what is the probability that 55 are or more areBharti Teletech customers?


4/15

` HR manager has chosen 10 samples each consists of50 employees

` We can compute sample statistic mean() for eachsample.` may be different for different sample.` A probability distribution of all possible means of the

samples is a distribution of the sample means-----Sampling Distribution of the mean.


5/15

` SD of the sample mean of the samplingdistribution

` STANDARD ERROR`

The standard deviation of the distribution of asample statistics is known as the Standard Errorof the statistics.

` Indicates the accuracy we are likely to get if weuse a sample statistic to estimate a population

parameter.


6/15

SD of the distribution ofSD of the distribution ofsample meanssample means SE of meanSE of mean

SD of the distribution ofSD of the distribution of

sample mediansample median

SE of medianSE of median

SD of the distribution ofSD of the distribution of

sample proportionsample proportion

SE of proportionSE of proportion


7/15

` Indicates the accuracy we are likely to get if weuse a sample statistic to estimate a population

parameter.` A lower value of standard error-----` Value of SE when sample size increases---` What will be the shape of the sampling distribution

of sample mean with differently shaped populationdistribution?

`

Central Limit Theorem


8/15

`

The mean of the sampling distribution of the meanwill equal the population mean-

regardless of the sample size, even if the population

is not normal.

` As the sample size increases, the sampling

distribution of the mean will approach normality,

regardless of the shape of the population distribution.


9/15

` n30`

Sampling distribution of the sampling meanfollows a normal distribution.` Z formula will be

` Z= (sample mean- population mean)/sample SD(SE)

` SE=Population SD/ square root of the samplesize.

` Standard Error = /n` Z=(X-) / /n

x

xx

ZH

Y!


10/15

` The annual earnings of the employees of a cement

factory is normally distributed with mean of Rs

25,000and SD of Rs 3000. if the HR managerdraws a random sample of size 50, what is the

probability that their average earnings will be

more than Rs26,000?

` Population mean-25000,

` Population SD- 3000,

` n= 50,

` Sample mean= 26000.


11/15

` Infinite population

size-----

Standard Error =/n

1

x

N

nN

n

Finite population size----

Standard Error =


12/15

` In a Big bazaar, the mean expenditure per

customer is Rs 1850 with a SD of Rs 750. If a

random sample of 100 customers is selected, what

is the probability that the, sample average

expenditure per customer for this sample is more

than Rs 2000.

` Out of total production of razor blades in a day,

15% are found defective. What is the probability

of randomly selecting 90 razor blades and finding

10 or less defective.


13/15

` Data items time, weight, height, income

` Appropriate statistic Sample mean` Data item countable items- people who own car,` Appropriate Statistic sample proportion.` Researchers use sampling proportion to make

statistical inference about population proportion.


14/15

` Out of total production of razor blades in a day,

15% are found defective. What is the probability

of randomly selecting 90 razor blades and finding10 or less defective.

` Sample proportion= x/n= no. of item in a sample

possessing the given characteristics/ no of items inthe sample.

` SD of Sample proportion= (pq/n)` Z= Sample proportion- population proportion)/

(pq/n)


15/15

` Stansdard error` Sampling distribution of sample mean for infinite

population.

` Sampling distribution of sample mean for finitepopulation` Sampling distribution for sample proportion

Session 1- Sampling Distribution

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