Hypothesis testing of the difference between proportions, Mathematics

Hypothesis Testing Of The Difference Between Proportions

Illustration

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.

Required

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

Solution

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)}¦

Whereas:

 

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.

Π1

Π2

 

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¦  

=12.3

 

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

Millie purchased six bottles of soda at $1.15 each. How much did she pay? To ?nd out the total cost of six bottles, you must multiply the cost per bottle through 6; $1.15 × 6 =



miaty and yesenia have a group of base ten blocks.Misty has six more than yesnia. Yesenia''s blocks repersent 17 together they have 22 blocks,and the total of blocks repersent 85.

Explain Comparing Fractions with example? If fractions are not equivalent, how do you figure out which one is larger? Comparing fractions involves finding the least common

Brian's 100-yard dash time was 2.68 seconds more than one school record. Brian's time was 13.4 seconds. What is the school record? The school record is less than Brian's time.

Company A and Company B have spent a lot of money on research to develop a cure for the common cold. Winter is approaching and there is certainly going to be a lot of demand for th


Give all solutions between o degree and 360 degree for sin x=3/2