Hypothesis testing of the difference between proportions, Mathematics

Assignment Help:

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.

 


Related Discussions:- Hypothesis testing of the difference between proportions

Determine z-scores and percentiles, Q. Determine Z-scores and Percentiles? ...

Q. Determine Z-scores and Percentiles? Ans. Z-scores help measure how far a piece of data is from the mean. More specifically, Z-scores tell how far a piece of data is fr

Basic Mathematics, Distinguish between Mealy and Moore Machine? Construct a...

Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''''s encountered is even or odd.on..

Homework help, Eduardo is combining two 6 inches pieces of wood with a piec...

Eduardo is combining two 6 inches pieces of wood with a piece that measures 4 inches. How many total inches of wood does he have?

Area in polar cordinates, find the area of the region within the cardioid r...

find the area of the region within the cardioid r=1-cos

Parallel lines, Parallel to the line specified by 10 y + 3x= -2 In this...

Parallel to the line specified by 10 y + 3x= -2 In this case the new line is to be parallel to the line given by 10 y ? 3x ? -2 and so it have to have the similar slope as this

Accuray and Precision, If an instrument has precision of +-1, can it detect...

If an instrument has precision of +-1, can it detect a value of 1.3?

Calculate the amplitude of trigonometry function, Consider the trigonometri...

Consider the trigonometric function f(t) = -3 + 4 cos(Π/ 3 (t - 3/2 )). (a) What is the amplitude of f (t)? (b) What is the period of f(t)? (c) What are the maximum and mi

Algebra, solve for y 3x+4y=7

solve for y 3x+4y=7

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