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
Example of line - Common Polar Coordinate Graphs Example:  Graph θ = 3Π, r cos θ = 4 and r sin θ = -3 on similar axis system. Solution There actually isn't too much to



Solve 8 cos 2 (1 - x ) + 13 cos(1 - x )- 5 = 0 . Solution Now, as specified prior to starting the instance this quadratic does not factor.  Though, that doesn't mean all i

I need expert who can solve 10 set of PDE with constant of integration.

The height of a parallelogram measures 5 meters more than its base. If the area of the parallelogram is 36 m 2 , what is the height in meters? Let x = the measure of the base a

Q. Definition of Random Variables? Ans. Up to this point, we have been looking at probabilities of different events. Basically, random variables assign numbers to element

A shuttlecock used for playing badminton has the shape of a frustum of a Cone mounted on a hemisphere.  The external diameters of the frustum are 5 cm and 2 cm, and the height of t


what is into function?