Estimation of population proportions, Mathematics

Estimation of population proportions

This form of estimation applies at the times while information cannot be described as a mean or as a measure but only as a percentage or fraction ,The sampling theory stipulates that if repeated large random samples are consider from a population and the sample proportion "p' will be normally distributed along with mean equal to the population proportion and standard error equal to

Sp = √{(pq)/n}  = Standard error for sampling of population proportions

Whereas n is the sample size and q = 1 - p.

The procedure for estimation a proportion is similar to that for estimating a mean; we simply have a different formula for calculating standard.

Illustration 1

In a sample of 800 candidates, 560 were male. Estimate the population proportion at 95 percent confidence level.

Solution

Now

Sample proportion (P) = 560/800  = 0.70

            q = 1 - p = 1 - 0.70  = 0.30

            n = 800

              √{(pq)/n} = √{(0.70)(0.30)/800} 

Sp = 0.016

Population proportion

= P ± 1.96 Sp whereas 1.96 = Z.

= 0.70 ± 1.96 (0.016)

= 0.70 ± 0.03

= 0.67 to 0.73

= between 67 percent to 73percent

Illustration 2

A sample of 600 accounts was taken to test the accuracy of posting and balancing of accounts whereas in 45 mistakes were found. Determine the population proportion. Employ 99 percent level of confidence

Solution

Now

n = 600;  p = 45/600  =  0.075

            q = 1 - 0.075 = 0.925

√{(pq)/n} = √{(0.075)(0.925)/600} 

= 0.011

Population proportion

= P ± 2.58 (Sp)

= 0.075 ± 2.58 (0.011)

 

= 0.075 ± 0.028

= 0.047 to 0.10

= between 4.7 percent to 10 percent

Posted Date: 2/19/2013 12:34:14 AM | Location : United States







Related Discussions:- Estimation of population proportions, Assignment Help, Ask Question on Estimation of population proportions, Get Answer, Expert's Help, Estimation of population proportions Discussions

Write discussion on Estimation of population proportions
Your posts are moderated
Related Questions

Assume that Y 1 (t) and Y 2 (t) are two solutions to (1) and y 1 (t) and y 2 (t) are a fundamental set of solutions to the associated homogeneous differential equation (2) so, Y

Each Child Is Unique :  Although every child goes through similar stages of development, the process may vary from one set of children to another, and also from one child to anoth

A radiograph is made of an object with a width of 3 mm using an x-ray tube with a 2 mm focal spot at a source-to-film distance of 100 cm. The object being imaged is 15 cm from the

find a30 given that the first few terms of an arithmetic sequence are given by 6,12,18...

A piece of cardboard in the shape of a trapezium ABCD & AB || DE, ∠ BCD = 900, quarter circle BFEC is removed. Given AB = BC = 3.5 cm, DE = 2 cm. Calculate the area of remaining p

A man can do a piece of work in 25 days how many people are required to complete same work in 15 days?


a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit

I need help with pre algebra in 5th grade intermidate school math until Tuesday afternoon please