Mat 13 Worksheet (12e Triola & Internet Sources/compiled by N. Sinb) May 201 CHA

Question

Mat 13 Worksheet (12e Triola & Internet Sources/compiled by N. Sinb) May 201 CHAPTER 11 Goodness-of-Fit and Contingency Tables 8 1. A particular brand denote as: of candy-coated chocolate comes in five different colors that we shall .A (brown) A2-(yellow) .A(orange) A4- (green) .As-{coffee) pi equal the probability that the color of a piece of candy selected at random belongs to Ho:p(brown) 0.4; p(yellow) 0.2; p(orange) -0.2 Ha: proportions not specified in the null Let A, for i-1,2 3, 4, 5. Test the following null and alternative hypotheses at sig. level of 0 p(green)- 0.1; p(coffee) 0.1 Categories Brown Yellow Orange Green Coffee Total Observed (y) 224 119 130 48 59 580 Assumed Ho (p)0.4 0.2 0.2 0.1 0.1 1.0 (Ans x'statistic 3.784;x2 critical 9.488)

Explanation / Answer

Here first we will calculate the expected value for each color chocolate

so the expected values are

Brown = 580 * 0.4= 232

Yellow = 580 * 0.2 = 116

Orange = 580 * 0.2 = 116

Green = 580 * 0.1 = 58

Coffee = 580 * 0.1 = 58

Here now the chi-square statistic

X2= (224 - 232)2/232 + (119 - 116)2/116 + (130 - 116)2/116 + (48 - 58)2/58 + (59 - 58)2/58 = 3.7845

Here at the significance level 0.05

X2 < X2critical

so we fail to rejct the null hypothesis and can conclude that theobserved data is in coformity to the proportion of choclate colors.

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