quants estimation

8/8/2019 Quants Estimation

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A PRESENTATION

ON

ESTIMATION

PRESENTED BY :PRAVEEN KR. SINGH(M/34)RAHUL PANDEY(M/37)SHIVENDER BHARGAV(M/51)U.PRABIR JAISWAL(M/61)ASHUTOSH SHARMA(M/67)


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AN ESTIMATE IS A VALUATION BASED ON

OPINION OR ROUGHLY MADE FROM

IMPERFECT OR INCOMPLETE DATA.

WE STUDY ESTIMATES SO THAT WE CAN

LEARN ABOUT POPULATION BY

SAMPLING, WITHOUT COUNTING EVERYITEM IN THE POPULATION

ESTIMATION


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UNBIASED

EFFICIENCY

CONSISTENCY

SUFFICIENCY

CRITERIA OF A GOOD ESTIMATOR


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POI I : POI I

I I

I OF POPULATIONPARAMETER

INTERVALESTIMATE:AN INTERVALESTIMATE ESCRI ESARANGEOF

VALUES ITHIN HICHAPOPULATION

PARAMETER ISLIKELYTOLIE.

TYPESOFESTIMATES


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Estimate PopulationParameter...

with SampleStatistic

Mean Q

Proportion p ps

Variance s2

Population Parameters

Estimated

W2

X_

__


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90% Samples

95% Samples

Wx_

Confidence Intervals

xx.. WQWQ 64516451

xx WQWQ 96.196.1

xx.. WQWQ 582582

99% Samples

nZXZX

X

WW ys!ys

X

_


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Mean

Confidence

Intervals

Proportion

Finite

PopulationW Known

Confidence Interval Estimates


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FROM A POPULATION OF 140007531 ,ASAMPLE OF 37 YEARS IS TAKEN. FROM THIS

SAMPLE THE MEAN IS FOUND TO BE 94.9726

, AND THE STANDARD DEVAITION 125.03.

1. FIND THE ESTIMATED STANDARD ERROR

OF THE MEAN.

2. CONSTRUCT 95% CONFIDENCE INTERVAL

FOR THE MEAN

3. CONSTRUCT 99% CONFIDENCE INTERVAL

FOR THE MEAN.

CASE ONE


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HERE,

STANDARD ERROR = 20.55

STANDARD DEVIATION = 125.03

MEAN = 94.9726

POPULATION = 140007531

AT 95% CONFIDENCE LEVEL, VALUE WILL LIE

BETWEEN 54.72 TO 135.24

AT 99% CONFIDENCE LEVEL, THE VALUE WILL LIE

BETWEEN 41.96 TO 147.98

SOLUTION :


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CASE TWO(2)

Find a 95% confidence interval forp, the proportion of smallbusinesses in favor of a taxincrease to decrease the national

debt, if a random sample of 1000found the number of businesses infavor of increased taxes was 50.


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Solution

50 .05, .95and the confidence1000

interval is

(.05)(.95).05 1.96 = .05 .0141000

(.036, .064)

p so q! ! !

s s


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InterpretingConfidence Intervals

Correct: We are 95% confident that theinterval from .036 to .064 actually doescontain the true value of p. This means

that if we were to select many differentsamples of size 1000 and construct a 95%CI from each sample, 95% of the resultingintervals would contain the value of the

population proportion p. (.036, .064) isone such interval. (Note that 95% refersto the procedure we used to constructthe interval; it does not refer to the

population proportion p)


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WRONG: THERE IS A 95%

CHANCE THAT THE POPULATIONPROPORTION P FALLS BETWEEN

.036 AND .064. (NOTE THAT P IS

NOT RANDOM, IT IS A FIXED BUTUN NOWN NUMBER)


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THE AVERAGE MONTHLY ELECTRICITY

CONSUMPTION FOR A SAMPLE OF 100

FAMILIES IS 1250 UNITS. ASSUMING THE

STANDARD DEVIATION OF ELECTRICCONSUMPTION OF ALL FAMILIES IS 150

UNITS, CONSTRUCT A 95 PERCENT

CONFIDENCE INTERVAL ESTIMATE OFTHE ACTUAL MEAN ELECTRIC

CONSUMPTION.

CASE 3 (THREE)


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THE INFORMATION GIVEN IS :

CONFIDENCE LEVEL (1- )= 95 PERCENT.

AT 95 % CONFIDENCE INTERVAL, Z= 1.96

X z /n =1250 1.96 *150/100=125029.40

Thus for 95% level of confidence,the populationmean is likely to fall between 1220.60 units and1274.40 units ,that is, 1220.60 1274.40


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A SMALL LOCAL BAN HAS 1450INDIVIDUALS SAVINGS ACCOUNTS WITH

AN AVERAGE BALANCE OF RS 3000 AND

A STANDARD DEVIATION OF RS 1200.IFTHE BAN TA ES A RANDOM SAMPLE

OF 100 ACCOUNTS, WHAT IS THE

PROBABILITY THAT THE AVERAGESAVINGS FOR THESE 100 ACCOUNTS

WILL BE BELOW RS 2800.

CASE (FOUR)


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= -1.73

SOLUTION


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What sample size is needed to be 90%

confident of being correct within 5? A pilot

study suggested that the standard deviation is45.

nZ

Error! ! ! $

2 2

2

2 2

2

1645 45

5

219 2 220W .

.

CASE(FIVE) Sample Size for Mean

Round Up


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What sample size is needed to be within 5 with

90% confidence? Out of a population of1,000, we

randomly selected 100 of which 30 were defective.

CASE(SI )Sampl Siz f r Pr portion

Round Up

3227

05

703064511

2

2

2

2

.

.

))(.(..

error

)p(pZn !!

!

228$


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SOURCES

TOYOTA MOTORS(SALES AND PRODUCTION)


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quants estimation

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