# LL9 - Part 9 Chi-square Tests 1. Goodness-of-fit Tests 2....

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BUS1200-9 1 Part 9 Chi-square Tests 1. Goodness-of-fit Tests 2. Tests of Independence: Contingency Tables Section 9.1 Goodness-of-fit Tests Example 1 A journal reported that, in a bag of M&M chocolate peanut candies, there are 30% brown, 30% yellow, 10% blue, 10% red, 10% green and 10% orange candies. Suppose you purchase a bag of M&M chocolate peanut candies at a nearby store and find 17 brown, 20 yellow, 13 blue, 7 red, 6 green and 9 orange candies, for a total of 72 candies. Does the bag purchased agree with the distribution suggested by the journal? Objective of a goodness-of-fit test : to find out how well a set of observed frequencies fits a set of expected frequencies calculated according to a specified distribution. The hypotheses considered are BUS1200-9 2 H 0 : the population follows a specified distribution, H 1 : the population does not follow the specified distribution stated in H 0 . Suppose the whole population can be divided into k categories. We reject H 0 if and only if = k i i i i e e o 1 2 ) ( χ 2 α , k 1 where the left-hand side is the value of the test statistic for the test, the right-hand side is the critical value, is the significance level, o i is the observed frequency for the i th category of the population and e i is the corresponding expected frequency calculated by e i = Sample size × Corresponding probability in the distribution specified by H 0 . The value of 2 , n can be obtained from the chi-square distribution table . BUS1200-9 3 Graphs of Density Functions of the 2 Distribution (“df” for degrees of freedom) The rule introduced here is only an 0 0.2 0.4 0.6 0.8 246 8 df = 1 df = 2 df = 3 df = 4 df = 5 df = 10 df = 15 df = 20 df = 25 df = 30 0.02 0.04 0.06 0.08 0 10 20 30 40 50 Density function of the 2 distribution with n degrees of freedom Area = 2 ,n 0 BUS1200-9 4 approximate result. It is suggested that all

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## LL9 - Part 9 Chi-square Tests 1. Goodness-of-fit Tests 2....

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