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Exercise 2 You are given the task of sampling the household size of customers at a grocery store and the number of bananas they buy. (a) You collect 150 observations. The relative frequency is fix = 4y = 2) = 1/18 and the absolute frequency is h(x = 2 y = 3)= 30. Based on this information, fill in the missing cells below. 1 person (y = 1) 20 >3 persons (y = 3) 2 persons (y = 2) 30 20 Sum (x) 60 O bananas (x = 1) 1 bananas (x = 2) 2 bananas ( x3) >3 bananas (x = 4) Sum (y) 55 27 20 33 54 4.8 Chapter Exercises 121 (b) The data you collect yields the following contingency table. Fill in the marginal frequencies and the expected counts under statistical independence. In the parentheses, provide the expected counts given the actual number of observations. Sum (x) O bananas (x = 1) 1 Banana (x = 2) 2 bananas (x = 3) >3 bananas (x = 4) Sum (y) 1 person (y = 1) 40 ) 103 5 20 2 persons (y = 2) 00 15 00 OC 3 persons (y = 3) 40 87 3 5) (c) Determine the chi-square value. (d) Calculate Cramer's V. (e) Why doesn't it make sense to calculate phi in this case? Exercise 3 A company measures customer satisfaction in three regions, producing the following crosstab: Customer satisfaction Region Region 1 13 6.1 86.7% Excellent Region 2. 0 5.5 0.0% Region 3 2 3.5 13.3% Total 15 15.0 100.0% 61.9% 25.0% Average 0 0.0% 0.0% 10 7.3 50.0% 16.7% 3.8% 10 4.6 50.0% 28.8% 28.8% 20 20.0 100.0% 8.1 0.0% 0.0% 0.0% 52.6% 19.2% Count Expected count % within customer satisfaction % within region % of total Count Expected count % within customer satisfaction % within region % of total Count Expected count % within customer satisfaction % within region % of total Count Expected count % within customer satisfaction % within region % of total 83.3% 19.2% 0 Poor 8 9 38.5% 38.5% 17 17.0 100.0% 6.9 47.1% 6.2 52.9% 3.9 0.0% 0.0% 0.0% Total 38.1% 15.4% 21 21.0 40.4% 47.4% 17.3% 19 19.0 36.5% 12 12.0 23.1% 32.7% 32.7% 52 52.0 100.0% 100.0% 40.4% 100.0% 36,5% 100.0% 23.1% 100.0% 100.0%