Chi square test as a test of independence, Financial Management

Chi Square Test as a Test of Independence

In real life decision making, managers often have to know whether the differences between the proportions observed from a number of samples are serious enough to be probed further. In other words, a decision has to be taken whether these differences are significant enough to warrant setting up the hypothesis and testing it or whether they are due to chance. This is mandatory as it has a bearing on the future of the firm. We understand this further by taking an example. A brand manager of an FMCG wants to know whether the revenue from the sale of a product is uniform throughout the country or not. For this, he collects the data by conducting a survey consisting of 1000 consumers from each of the four zones. He arranges the data in rows and columns by classifying it in terms of the geographical location and whether the consumer purchases that particular brand or not. The significance level he chose was a = 10%. The data collected by him is as follows:

 

 

Zones

Total

Northern

Western

Southern

Eastern

Purchase the brand

Do not purchase the brand

400

600

550

450

450

550

500

500

1900

2100

Total

1000

1000

1000

1000

4000

The table shown above is referred to as contingency table whose order is 2 x 4. That is, the table consists of two rows and four columns. We do not consider the row and the column under the head "total".

Setting up the Hypothesis

If the proportions of the total population of consumers in each of the four zones are denoted by pN, pw, pS and pE, then the null and the alternative hypothesis will be set up as follows:

H0:    pN = pW = pS = pE        (Null hypothesis: Proportion of consumers from each of the four zones are equal)

H1:    pN  ≠ pW   ≠  pS   ≠  pE    (Alternative Hypothesis: Proportion of consumers from each of the four zones are not equal)

If we accept the null hypothesis, the total proportion of the consumers buying the product can be calculated. In our example it is given by

2331_chi square test.png 1900/4000 = 0.475

 

Then the number of consumers who would not buy the product is 1 - 0.475 = 0.525. Using these two proportions, we can calculate the proportion of consumers who would either buy or not buy the product in each of the four zones. These figures give us the expected frequencies. They are shown in the table below.

 

Zones

 

Northern

Western

Southern

Eastern

Purchase the brand

1000 x 0.475
 = 475

1000 x 0.475
 = 475

1000 x 0.475
 = 475

1000 x 0.475
 = 475

Do not purchase the brand

1000 x 0.525
 = 525

1000 x 0.525
 = 525

1000 x 0.525
 = 525

1000 x 0.525
 = 525

Posted Date: 9/15/2012 5:56:35 AM | Location : United States







Related Discussions:- Chi square test as a test of independence, Assignment Help, Ask Question on Chi square test as a test of independence, Get Answer, Expert's Help, Chi square test as a test of independence Discussions

Write discussion on Chi square test as a test of independence
Your posts are moderated
Related Questions
The following guidelines are applicable for the issue of Fully Convertible Debentures (FCDs), Partly Convertible Debentures (PCDs) and Non-conve

• Debtors :- Working Capital tied up in debtors must be estimated on the basis of cost of sales (excluding depreciation): [Cost of goods produces (that is raw materials + wages

How can funds be raised Funds are raised from financial markets. Financial markets is a general term used todenote markets where financial securities are teat. These markets in

Credit Markets: The financial system enables supply of funds to support purchase of goods and services and to finance capital investments. In this way, it provides funds both t

Simple Arbitrage The easiest arbitrage opportunities in the option market exist when options violate simple pricing bounds. No option, for example, should sell for less than it

Q. Evaluae new options within current organization? Evaluating having completed self marketing successfully to prospective employers it is time to analyze new options within cu

What is the Ratios based on historic cost accounts Ratios based on historic cost accounts don't give a true picture of trends, due to the effects of inflation and different acc

Principal repayment before the scheduled date is called a prepayment. Every individual borrower normally has the option to pay off all or part of their loan

Explain the aspects of financing decision The financing decision covers two interrelated aspects: (1) capital structure theory (2) capital structure decision.

Dividend Decision: The Dividend Decision is a decision taken by the directors of a company. It relates to the timing of any cash payments and amount made to the company's stoc