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

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

Tom is cutting a piece of wood to form a shelf. He cut the wood to 3.5 feet, but it is too long to fit in the bookshelf he is forming. He decides to cut 0.25 feet off the board. Ho


Ask question what is half of 1 1/3 liquid measurements?

a circle is circumscribed about an equilateral triangle whose side is 3 cm. find the area of the circle.

The Mean Value Theorem  Assume f(x) is a function that satisfies both of the subsequent. 1.   f(x) is continuous on the closed interval [a,b]. 2.   f(x) is differentiabl

Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers

how can i solve it

Ask question #Minimum 100 words accepted linear algebra