Hypothesis testing about the difference between two proporti, Mathematics

Assignment Help:

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.


Related Discussions:- Hypothesis testing about the difference between two proporti

Statistics, what is meant by "measure of location"

what is meant by "measure of location"

Binary, how to divide a binaries

how to divide a binaries

Round this number to the closest thousandth, It takes the moon an average o...

It takes the moon an average of 27.32167 days to circle the earth. Round this number to the closest thousandth. The thousandths place is the third digit to the right of the dec

rules for solving linear in-equations - linear algebra, Explain what are t...

Explain what are the Rules for solving linear in-equations?

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

How do children learn maths?, HOW DO CHILDREN LEARN? : Have you ever tried...

HOW DO CHILDREN LEARN? : Have you ever tried teaching a young child what "ball" means? Did you do it by a lot of verbal description" Or did you let the child actually handle a b

Determine the differential y = t 3 - 4t 2 + 7t, Determine the differentia...

Determine the differential for following.                                      y = t 3 - 4t 2 + 7t Solution Before working any of these we have to first discuss just

Differential equations, Verify Liouville''''''''s formula for y "-y" - y'''...

Verify Liouville''''''''s formula for y "-y" - y'''''''' + y = 0 in (0, 1) ?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd