Hypothesis testing about the difference between two proporti, Mathematics

Hypothesis Testing About The Difference Between Two Proportions

Hypothesis testing about the difference between two proportions is used to test the difference between the proportions of a described attribute found in two random samples.

The null hypothesis is that there is no difference between the population proportions. It means two samples are from the same population.

Hence

H0 : π1 = π2

The best estimate of the standard error of the difference of P1 and P2 is given by pooling the samples and finding the pooled sample proportions (P) thus

P =  (p1n1 + p2n2)/ (n1 + n2)

Standard error of difference between proportions

S(P1 - P2) = √{(pq/n1) + √(pq/n1)}   

       And Z = ¦ {(P1 - P2)/S (P1 - P2)}¦

Illustration

In a random sample of 100 persons obtained from village A, 60 are found to be consuming tea. In another sample of 200 persons obtained from a village B, 100 persons are found to be consuming tea. Do the data reveal significant difference among the two villages so long as the habit of taking tea is concerned?

Solution

Assume us take the hypothesis that there is no significant difference among the two villages as much as the habit of taking tea is concerned that is: π1 = π2

We are given

      P1 = 0.6;     n1 = 100

      P2 = 0.5;     n2 = 200

 

Appropriate statistic to be utilized here is described by:

 

P = (p1n1 + p2n2)/ (n1 + n2)

  = {(0.6)(100) + (0.5)(200)}/(100 + 200)

= 0.53

q = 1 - 0.53

= 0.47

S(P1 - P2) = √{(pq/n1) + √(pq/n1)}   

            = √{((0.53)(0.47)/100) + ((0.53)(0.53)/200)}

            = 0.0608

Z = ¦ {(0.6 - 0.5)/0.0608}¦

      = 1.64

Because the computed value of Z is less than the critical value of Z = 1.96 at 5 percent level of significance therefore we accept the hypothesis and conclude that there is no significant difference among in the habit of taking tea in the two villages A and B t-distribution as student's t distribution tests of hypothesis as test for small samples n < 30

For small samples n < 30, the method utilized in hypothesis testing is exactly similar to the one for large samples except that t values are used from t distribution at a specified degree of freedom v, instead of Z score, the standard error Se statistic used is different also.

Note that v = n - 1 for a single sample and n1 + n2 - 2 where two sample are involved.

Posted Date: 2/19/2013 1:39:15 AM | Location : United States







Related Discussions:- Hypothesis testing about the difference between two proporti, Assignment Help, Ask Question on Hypothesis testing about the difference between two proporti, Get Answer, Expert's Help, Hypothesis testing about the difference between two proporti Discussions

Write discussion on Hypothesis testing about the difference between two proporti
Your posts are moderated
Related Questions
Need solution For the universal set T = {1, 2, 3, 4, 5} and its subset A ={2, 3} and B ={5, } Find i) A 1 ii) (A 1 ) 1 iii) (B 1 ) 1

Problem1: Find the general solution on -π/2 Dy/dx +(tan x)y =(sin 2 x)y 4

I didn't understand the concept of Technical Coefficients, provide me assistance.


Inverse Tangent : Following is the definition of the inverse tangent.  y = tan -1 x     ⇔ tan y = x                     for            -∏/2 ≤ y ≤ ?/2 Again, we have a limi

a triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius 3.what is the area of the triangle.

two circle of radius of 2cm &3cm &diameter of 8cm dram common tangent

Explain Equivalent Fractions ? Two fractions can look different and still be equal. Different fractions that represent the same amount are called equivalent fractions. Ar

Problem 1. Find the maximum and the minimum distance from the origin to the ellipse x 2 + xy + y 2 = 3. Hints: (i) Use x 2 + y 2 as your objective function; (ii) You c

Application of rate change Brief set of examples concentrating on the rate of change application of derivatives is given in this section.  Example    Find out all the point