A multinomial experiment with k = 3 cells and n = 320 produced the data shown in the following one-way table. Do these data provide sufficient evidence to contradict the null hypothesis that p1 = .25, p2 = .25, and p3 = .50? Test using a = .05. Cell 1 2 3 ni 78 60 182 L10004 *Note that focusing on one outcome has the effect of lumping the other 1k - 12 outcomes into a single group. Thus, we obtain, in effect, two outcomes—or a binomial experiment. M10_MCCL3396_14_GE_C10.indd 609 25/09/2021 19:37 610 CHAPTER 10 ● Categorical Data Analysis animals is selected. Answer the following questions based on this assumption.

a. Identify the categorical variable (and its levels) measured in this study.

b. Based on the percentages shown in the pie chart, how many sampled farmed animals would you expect to observe for each type of animal farming?

c. If the true percentages of each farming type are equal, how many sampled farmed animals would you expect to observe for each type of animal farming?

d. Specify the null and alternative hypotheses for testing whether the true percentages of each farming type are equal.

e. Calculate the x2 test statistic for testing the hypotheses in part

d. f. Give the rejection region for the test using a = .05. g. Use the results, parts e and

f, to make the appropriate conclusion. h. Find and interpret a 95% confidence interval for the proportion of sheep farming in New Zealand animal farming.