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Bangladesh University of Professionals

Prepared For Lt. Coln. Farid Alam Course Instructor Marketing Research Method Bangladesh University of Professionals. Prepared By Group no # 4 Amir Hamza Mohammad Kayes, Roll # 043 Kamalesh Chandra Ghosh, Roll # 024 Mohammad Tanvir Ahmmed Molla, Roll # 044.

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Bangladesh University of Professionals

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  1. Prepared For Lt. Coln. Farid Alam Course Instructor Marketing Research Method Bangladesh University of Professionals. Prepared By Group no # 4 Amir Hamza Mohammad Kayes, Roll # 043 Kamalesh Chandra Ghosh, Roll # 024 Mohammad Tanvir Ahmmed Molla, Roll # 044 Bangladesh University of Professionals

  2. CHI-SQUARE TEST

  3. T-distribution, z-distribution, chi-square test are those types of test by which researcher recognize the statistical notation associated with null hypothesis and alternative hypothesis. There are some factors that influence the choice of which method of statistical analysis to be used by the researcher. Introduction

  4. The square of a standard normal vitiate is known as chi square variate with one degrees of freedom. In other words, a test that statistically determines significance in the analysis of frequency distribution Definition

  5. Null hypothesis A statement about a status quo asserting that any change from what has been thought to be true will be due entirely to random error. Alternative Hypothesis A statement indicating the opposite of the null hypothesis. Few Related Term

  6. Nonparametric Statical Procedures Statistical procedures that use nominal or ordinal scaled data and make no assumption about the distribution of the population ( or sampling distribution ) . Degree of freedom The number of constraints or assumptions needed to calculate a statistical term Few Related Term

  7. Many times managers need to know whether the differences they observe among several proportions are significant or only due to chance. In such situation chi-square test is a good option to ascertain. Chi-square tests also enable us to test whether more than two population proportions can be considered equal or not. Why chi-square test

  8. To test the hypothetical of the population variance is equal or not. To test the Goodness of Fit. To test the independence of attribute. To test the homogeneity of independent estimate of the population variance When chi-square test

  9. Observed and Expected Frequencies : Details of this method say that on the basis of observed data of one population, similar data of another population can be estimated. Chi-square test can determine whether expected data are close to reality or not How chi-square works

  10. A IT based company has collected a sample data of customer’s attitude / opinion toward on line purchasing facilities. Respondents are given a choice between the present condition and in favor of online purchasing facilities: Example

  11. Ho : Gu(a) = Ut(a) = Mi(a) = Dh (a) {population preferring present condition} (Null hypothesis) H1 : Gu(a), Ut(a), Mi(a), Dh (a) are not all equal( Alternate hypothesis) Level of significance = .10 If null hypothesis is true, we can combine data from four samples and then estimate the proportion of the total customers that prefer present method as follows: 68+75+57+79 100+120+90+110 = 279/420 = 0.6643 So, as per null hypothesis, the proportion that prefer new method is 0.3357 (= 1 - .6643) If actual and expected data are put in a table, it shows as follow: Hypothesis

  12. Table 2: Actual and Expected Data

  13. Formula for chi-square statistic: X2 = (fo – fe) 2 fe Where, fo= Observed Frequency fe = Expected Frequency X2= Chi-Square Chi-Square Statistic

  14. X2 = 2.7638 Since value of chi-square is very small (2.764) and in the 90% confidence interval the tabulated value for 3 degrees of freedom is = 6.25, therefore null hypothesis is accepted here. Caculation Result

  15. The chi-square distribution is a probability distribution. Total area is 1.0. The curve is different for different degrees of freedom. The lesser is the degrees of freedom, the smaller is the chi-square value and the more accurate is the expected data. Number of degrees of freedom = (number of rows –1) x (number of columns –1) Chi-Square Distribution & Degrees of Freedom

  16. Chi-square test can also be used to decide whether a particular probability distribution is the appropriate distribution. It helps us to test whether there is a significant difference between an observed frequency distribution and a theoretical frequency distribution. Example: Ho = a binomial distribution with p=.40 is a good description of interview process H1= a binomial distribution with p=.40 is not a good description Level of significance = .20 Chi-Square as a Test of Goodness of Fit

  17. Chi-Square as a Test of Goodness of Fit

  18. Chi-square X2 = 5.0406 So, the null hypothesis is rejected.General rule for determining degrees of freedom in a Goodness-of-Fit test is first employ (k-1) rule and then subtract an additional degree of freedom for each population parameter that has to be estimated from the sample data. Here, we have four classes of observed frequencies (k=4). So, appropriate number of degrees of freedom is (k – 1) or 3. Result

  19. To work with chi-square test, we had to study well about null hypothesis, alternative hypothesis, degrees of freedom, parametric nonparametric data, ordinal, nominal, binomial, ratio scale, interval scale etc. And this is really interesting and important for the researcher. Conclusion

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