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RVUC- Statistics Short Note (2).doc

Conclusion reject the null hypothesis at alpha 005

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Conclusion Reject the null hypothesis at alpha ( )=0.05. Based on a sample mean of Br 950, the mean salary of a newly graduated student does not equal to Birr 1000. CHAPTER THREE CHI-SQUARE DISTRIBUTIONS Introduction Dear learner, so far we have been talking about analysis of variance. Let us now turn our face to the discussion of chi square distribution. A Chi-square distribution is a continuous distribution ordinarily derived as the sampling distribution of a sum of squares of independent standard normal variables. It is denoted by the symbol 2 and has a single parameter; the degree of freedom denoted by ν which stands for the mean of the chi-square distribution. To find the variance of chi-square distribution, you have to simply multiply the mean of the distribution by two (2ν). Thus, the mean and Variance depend on the degree of freedom. The distribution is based on a comparison of the sample of observed data (results) with the expected results under the assumption that the null hypothesis is true. It is a skewed distribution and only non negative values of the variable X 2 are possible. The skewness decreases as ν increases; and when V increases without limit it approaches a normal distribution. It extends indefinitely in the positive direction; with the area under the curve is 1.0. 19
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20 | P a g e Up on completion of the chapter, learner should be able to; Apply X 2 to test for equality of several proportions Apply X 2 to test for independence between two variables Apply X 2 to test for goodness of fit test for Binomial distribution Poisson distribution Normal distribution The areas of application X 2 distribution Testing for the equality of several proportions Test for independence between two variables Goodness of fit tests for Binomial, Poisson, and Normal distribution Test for the independence between two variables Dear learner, test for the independence between two variables is another area of application for X 2 distributions. A X 2 test of independence is used to analyze the frequencies of two variables with multiple categories to determine whether the two variables are independent. That is, the Chi-square distribution involves using sample data to test for the independence of two variables. The sample data are given in to a two way table called a contingency table. Because the X 2 test of independence uses a contingency table, the test is sometimes referred to as contingency analysis. The X 2 test is used to analyze, for example, the following cases: Whether employee absenteeism is independent of job dissatisfaction Whether colour preference is independent of sex Whether favourite drink is independent of religion. Illustration : A company planning a TV advertising campaign wants to determine which TV shows its target audience watches and thereby to know whether the choice of TV program an individual watches is independent of the individuals income. The table supporting this is shown below. Use a 5% level of significance and the null hypothesis.
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