Hypothesis testing of the difference between proportions, Mathematics

Hypothesis Testing Of The Difference Between Proportions


Ken industrial producer have manufacture a perfume termed as "fianchetto." In order to test its popularity or reputation in the market, the manufacturer carried a random surveyor study in back rank city whereas 10,000 consumers were interviewed after that 7,200 demonstrated preferences. The manufacturer moved also to area Rook town where he interviewed 12,000 consumers out of that 1,0000 demonstrated preference for the product.


Design a statistical test and thus use it to advise the manufacturer regarding the differences in the proportion, at 5 percent level of significance.


H0 : π1 = π2

H1 : π1 ≠ π2

The critical value for this two tailed test at 5 percent level of significance = 1.96.


Now Z = ¦{(P1 - P2) - (Π1 - Π2)/S(P1 - P2)}¦

But as the null hypothesis is π1 = π2, the second part of the numerator disappear that is

π1 - π2 = 0 which will usually be the case at this level.


Then Z = ¦ {(P1 - P2)/S (P1 - P2)}¦



Sample 1

Sample 2

Sample size

n1 = 10,000

n2 = 12,000

Sample proportion of success

P1 =0.72

P2 = 0.83

Population proportion of success.




Here S (P1 - P2) = √{(pq/n1) + √(pq/n1)}   


Whereas p = (p1n1 + p2n2)/ (n1 + n2)

And q = 1 - p;

∴ in our case

P = {10,000 (0.72) + 12,000 (0.83)}/(10,000 + 12,000)

= 84,000/22,000

= 0.78

∴ q = 0.22

S (P1 - P2) = √{(0.78(0.22)/10,000) + (0.78(12,000)/12,000)}

= 0.00894

= ¦(0.72 - 0.83)/0.00894¦  



As 12.3 > 1.96, we reject the null hypothesis however accept the alternative. The differences among the proportions are statistically significant. It implies that the perfume is more popular in Rook town rather than in Back rank city.


Posted Date: 2/19/2013 1:38:22 AM | Location : United States

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

Write discussion on Hypothesis testing of the difference between proportions
Your posts are moderated
Related Questions
1-tan^2 A/1+tan^2 = cos A - sinA/cos A

Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we

Magnitude - Vector The magnitude, or length, of the vector v → = (a1, a2, a3) is given by, ||v → || = √(a 1 2 + a 2 2 + a 2 3 ) Example of Magnitude Illus

help me with how to write sample of proportion using visual basic

Let us now look at some activities that can be organised with preschoolers to develop their ability to classify. 1. You could start by giving children different materials to pla

Assume that (xn) is a sequence of real numbers and that a, b € R with a is not eaqual to 0. (a) If (x n ) converges to x, show that (|ax n + b|) converges to |ax + b|. (b) Give

If the normal range is 65-10 mg/dl, then what percentage of values will fall in the normal group?

A rectangular container is 15 cm wide and 5 cm long, and contains water to a depth of 8 cm. An object is placed in the water and the water rises 2.3 cm. Determine the volume of the

Q. How to Subtract fractions with different denominators? Ans. As with adding fractions, you can't subtract unless the denominators are the same. Here is an example: 9/