Question

13 Niki Xu (20pts) Consider a standard package of it and white. Suppose that we ob following distribution: Type Regular count 24 Standard package of KitKats. There are three different kinds: regular, dark Suppose that we observed a simnie random sample of 60 Kitkats with the white Dark white Park 22 Regular We are curious about the distribution of these types, do all three types occur in equal proportion? Conduct a Chi-sq goodness of fitness at .05 significance. a. Hypothesis (5pts) Ho: Ha: b. Calculate test statistics (10pts) C. Conclusion (5pts)

Answer 1

H: P. = P2 = p; H: At least one of pi is different Significance level: a = 0.05 Test statistic: r = {(0-E) Where, O =Observed frequency E = Expected frequency The below table describes the computation of chi square test statistic: (O - E) observed 24 14 22 Total 60 expected 20.000 20.000 20.000 60.000 O-E 4.000 -6.000 2.000 0.000 0.800 1.800 0.200 2.800 Therefore, the chi-square test statistic is xã = 2.800

Degree of freedom: df =n-1 = 3-1 = 2 P-value approach: p=P(x >x) = CHIDIST (2.800,2) [From Excel function] = 0.2466 Compare the p-value with significance level: Reject H, if p-value is less than significance level or otherwise. Since the p-value (0.2466) is greater than the significance level (0.05), so we fail to reject the null hypothesis. Conclusion: There is not sufficient evidence to warrant the rejection of the claim that the distribution of all three types occur in equal proportion.