# Question: 1 A product line is sold in 15 different configurations

1. A product line is sold in 15 different configurations of packaging. How does the large number of package types influence the value of the chi-squared statistic?

2. Why are chi-squared statistics not directly comparable between tables of different dimensions when the null hypothesis of independence holds?

3. Could Cramer’s V (Chapter 5) have been used rather than p-values to standardize the results? Give an advantage and a disadvantage of p-values compared to Cramer’s V statistics.

4. Of the 650 products, 69 come in 5 types of packaging. If packaging type and location are independent, what should be the average value of these 69 chi-squared statistics?

5. Suppose managers evaluate the association between package type and location for 50 products for which these are independent attributes. The data in each table are independent of the data in other tables.

a. How many of these 50 p-values would be expected to be less than 0.05?

b. What is the probability that at least one p-value would be less than 0.01?

c. If the smallest p-value is less than 0.01, should we conclude that package type and location for this product are associated?

6. The data used in the chi-squared analysis has 200 cases for each location. Is it necessary to have the same number of observations from each location for every product?

7. The histogram of p-values (Figure 4) shows that 84 products have p-value less than 0.025. Does this mean that if we were to examine all of the transactions for these products that we would find Location and Package Type associated for all 84 of them?

8. Explain how the analysis of packaging types could be used to manage the mix of colors or sizes of apparel in clothing stores that operate in different parts of the United States.

2. Why are chi-squared statistics not directly comparable between tables of different dimensions when the null hypothesis of independence holds?

3. Could Cramer’s V (Chapter 5) have been used rather than p-values to standardize the results? Give an advantage and a disadvantage of p-values compared to Cramer’s V statistics.

4. Of the 650 products, 69 come in 5 types of packaging. If packaging type and location are independent, what should be the average value of these 69 chi-squared statistics?

5. Suppose managers evaluate the association between package type and location for 50 products for which these are independent attributes. The data in each table are independent of the data in other tables.

a. How many of these 50 p-values would be expected to be less than 0.05?

b. What is the probability that at least one p-value would be less than 0.01?

c. If the smallest p-value is less than 0.01, should we conclude that package type and location for this product are associated?

6. The data used in the chi-squared analysis has 200 cases for each location. Is it necessary to have the same number of observations from each location for every product?

7. The histogram of p-values (Figure 4) shows that 84 products have p-value less than 0.025. Does this mean that if we were to examine all of the transactions for these products that we would find Location and Package Type associated for all 84 of them?

8. Explain how the analysis of packaging types could be used to manage the mix of colors or sizes of apparel in clothing stores that operate in different parts of the United States.

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