Exam 3 Review - Exam 3 Review Do plain and peanut m&m's...

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Exam 3 Review Do plain and peanut m&m's have the same distribution of colors? Several bags of each variety (plain and peanut) m&m’s were randomly selected, and the number of candies of each color was counted before eating any of them. The data appears below. brown yellow red blue Total plain 81 84 41 17 223 peanut 17 7 27 13 64 Total 98 91 68 30 287 1.What are the response and explanatory variables ? Ans : Response variable: Explanatory variable : 2. What should be the null and alternative hypotheses in this context ? Ans : H 0 : is independent of of peanut.
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Ha : Color and variety of peanut are associated. 3.Find the conditional distribution of color for peanut m&m’s. Ans : In order to do this we have to evaluate the conditional percentages as follows : brown yellow red blue Total plain 81/223= 36.32% 84/223 = 37.67% 41/223= 18.39% 17/223= 7.62% 223 peanut 26.56% 10.94% 42.19% 20.31% 64 Total 98 91 68 30 287 So, the required conditional distribution will be ( ) 4.What is the expected cell frequency red peanut Ans : Red peanut m&m’s : Brown plain m&m’s :
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Interpretation : If of m&m’s was independent of of m&m’s then there would have been about red peanut m&m’s and about brown 5.Are the assumptions of a Chi-square test satisfied for the above problem? Ans : , since the expected frequencies for all the cells are than . 6.What is the degrees of freedom of a Chi-square statistic ? Ans : Since we have rows and columns, the df will be 7. Suppose the p – value of the Chi-square test lies between 0.05 and 0.1. What will be your conclusion ? Ans : We would reject H 0 at level of significance but NOT at level. So, the observed data indicate that there is a significant association between color and type of m&m’s at the significance level but they are independent at the level.
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8. What is the residual for blue plain peanut ? Interpret. Ans : The observed frequency for this cell is and the expected frequency is .So, the residual will be This means that there are blue plain m&m’s in the sample than expected if color and variety (of m&m’s) were Data collected to study the relationship between child
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This note was uploaded on 04/18/2008 for the course EXP 3116 taught by Professor Fasig during the Spring '08 term at University of Florida.

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Exam 3 Review - Exam 3 Review Do plain and peanut m&m's...

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