The term churn is very important to managers in the cellular phone business. Churning occurs when a customer stops using one companys service and switches to another companys service. Obviously, managers try to keep churning to a minimum, not only by offering the best possible service but also by trying to identify conditions that lead to churning and taking steps to stop churning before it occurs. For example, if a company learns that customers tend to churn at the end of their two-year contract, the company could offer customers an incentive to stay a month or two before the end of their two-year contract. A particular cellular phone company has collected data on a sample of its customers. The data file C03_03.xlsx contains data on over 2000 customers. Each row contains the activity of a particular customer for a given time period, and the last column indicates whether the customer churned during this time period. The company is trying to learn everything it can to keep churning to a minimum. You can help by solving the following problems and then, based on your analysis, presenting a report to the company with recommendations. 1. The company wonders whether the period a customer has been using the company's service (Account Length) has anything to do with the churning. a. Calculate a 95% confidence interval for the mean account length of all customers who churn from the company. Do the same for those who do not churn. Then, calculate a 95% confidence interval for the difference between these means. (3) b. Among all customers whose account length is below the median (101 months), calculate a 95% confidence interval for the proportion who does not churn. Do the same for the customers with account lengths above the median. Then, calculate a 95% confidence interval for the difference between these proportions. (3) 2. The company wonders whether a customer has an international plan or a voice mail plan might influence who stays and who leaves. a. Among all customers who have an international call plan, calculate a 95% confidence interval for the proportion who does not churn. Do the same for the customers without an international call plan. Then, calculate a 95% confidence interval for the difference between these proportions. (3) 2 b. Repeat a, but now do the analysis in terms of voice mail plan rather than international plan. (3) 3. Among the calls received at customer service are complaints of unsatisfied customers. Responses to a customers enquiries and complaints and the number of times a customer calls the service could affect the customers decision on churning. One question can then be asked: Does the number of customer service calls made by a customer influence the churning? Calculate one or more relevant confidence intervals to help you make an argument one way or the other. (5) 4. Using the results of Questions 1 to 3 and the results of correlations, scatterplots, and regression analysis on the following, a. Relationship between international call charge and day charge, (1) b. relationship between international call charge and evening charge, and (1) c. relationship between international call charge and night charge. (1) What recommendations would you make to the company to reduce churn? (10)