Chi square test as a distributional goodness of fit, Applied Statistics

Assignment Help:

Chi Square Test as a Distributional Goodness of Fit

In day-to-day decision making managers often come across situations wherein they are in a state of dilemma about the application of a suitable distribution for the data they have. This assumes importance in the light that in this age one cannot afford to make mistakes which would put the firm in a disadvantageous position. Under these circumstances, managers can employ the Chi Square distribution to verify the appropriateness of the distribution employed by them and conclude whether any significant difference exists between the observed (actual) and the theoretical distribution they have employed. We look at the steps constituting this.

1. Setting up the hypothesis and the computation of the observed and the theoretical frequencies:

This step consists of setting up the hypothesis and arriving at calculated fo and the corresponding fe from the table.

2. Finding the value of the chi square statistic:

         The Chi Square statistic is given by

814_chi square test.png

         where,   

                   fo is the observed frequency

                   fe is the expected frequency.

3. Determining the degrees of freedom for the distribution:

We obtain the same in this case by applying the (k - 1) rule, where 'k' refers to the number of points we have sought to compare while calculating observed and theoretical frequencies. This has to be further reduced by the number of parameters one wishes to estimate from the sample statistics.

4. Referring the tables for the c2 statistic at (k - 1) number of degrees and ' α ' level of significance:

In this step, we refer the tables for the c2 statistic at (k - 1) degrees of freedom and required level of significance.

5. Accepting or rejecting the null hypothesis: In this step, one determines whether the computed statistic falls in the accepted region or not and accordingly accepts or rejects the null hypothesis.   


Related Discussions:- Chi square test as a distributional goodness of fit

Standard cost method, Under the standard cost method which is also referred...

Under the standard cost method which is also referred as the standard cost method ,stock receipts are assigned a standard cost. Any variations between the actual cost and standard

Uncertain demand, Consider a Cournot duopoly with two firms (fi rm 1 and f...

Consider a Cournot duopoly with two firms (fi rm 1 and fi rm 2) operating in a market with linear inverse Demand P(Q) = x Q where Q is the sum of the quantities produced by both

Harmonic mean, Harmonic Mean  The harmonic mean  also called harmonic  ...

Harmonic Mean  The harmonic mean  also called harmonic  average, in the total numbers of items of variable divided by the sum of r reciprocals of the values of the variable. In

Quote, How much would u charge for 4 questions

How much would u charge for 4 questions

Types of sampling, Given a certain population there are various ways in whi...

Given a certain population there are various ways in which a sample may be drawn from it. The chart below illustrates this point: Figure 1 In  Judgem

Stat, solve problems

solve problems

Explain graph theory, For each of the following scenarios, explain how grap...

For each of the following scenarios, explain how graph theory could be used to model the problem described and what a solution to the problem corresponds to in your graph model.

Evaluation tracking system, BCBSRI was able to reduce MSD related Workers C...

BCBSRI was able to reduce MSD related Workers Compensation cases with lost workdays by implementing a New Ergonomic Program in March 2000 and increasing workstation evaluations. Ex

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