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
consumer behaviour in my feild of studies accounting ..

Relationship between the inverse sine function and the sine function We have the given relationship among the inverse sine function and the sine function.

Test of hypothesis about the population mean When the population standard deviation (S) is identified then the t statistic is defined as             t = ¦(x¯ - µ)/ S x¯ ¦

how to solve fraction word problems

what does 4/100+1/10=

Q) In 3D-geometry give + and - signs for x,y,z, in all eight octants Ans) There is no specific hard rule for numbering the octants. So, it makes no real sense to ask which octan

I had just come back from a very interesting talk arranged by a Mathematics Centre, it was aimed at parents of primary school-going children. They had talked about, and demonstrate

The square of a positive number is 49. What is the number? Let x = the number.  The sentence that is , "The square of a positive number is 49," translates to the equation x 2

We know that one has to deal with numbers in day-to-day life irrespective of his inclination and field of work. Also one cannot refute the fact

A discrete-valued random variable X takes values in 0, 1, 2, . . . , where p(X = i) = π i. (a) Write down formulas for: the p-value at X = i the probability distributi