1. (Note: Use a = 0.05 for all tests) The Bank Call Center data shows the data on 70 former employees at one of the bank's call centers. a. Is the average length of service for all employees shorter than 2 years? 1. What are the null and alternative hypotheses? 2. Pick the correct test and calculate the test statistics. 3. Is the alternative hypothesis supported? Why? b. Is the average length of service for individuals without a college degree the same as those with a college degree? 1. What are the null and alternative hypotheses? 2. Pick the correct test and calculate the test statistics. 3. Is the alternative hypothesis supported? Why? c. Are employees actual length of service shorter than their planned length of service? 1. What are the null and alternative hypotheses? 2. Pick the correct test and calculate the test statistics. 3. Is the alternative hypothesis supported? Why? 2. Using the data in the Excel file Home Market Value, develop a multiple linear regression model for estimating the market value as a function of both the age and size of the house. Predict the value of a house that is 30 years old and has 1,800 square feet, and one that is 5 years old and has 2,800 square feet. 3. The Excel file Vacation Survey provides information about 34 respondents age, gender, relationship status, number of children and vacations per year. a. Develop a multiple regression model for predicting vacations per year as a function of the other variables. b. Explain how age, gender, relationship status and number of children affect the number of vacations taken per year. (Is gender a significant predictor at a = 0.05? How about when a =0.1? Explain the effect of gender at a =0.1) 4. The coal consumption data shows the monthly coal consumption (in trillions of BTUs) over the course of three years. a. Create a line chart for the demand data overtime, what pattern do you observe? b. Develop a multiple regression model with variable month and categorical variables that incorporate seasonality for forecasting coal consumption, where December is the reference month. (Hint: run the regression analysis and write out the equation of the predictive model for coal consumption). c. Was the effect of month significant at a = 0.05? Whats the effect of month on coal consumption? What does it mean? d. Based on your multiple regression model, predict the coal Consumption in March 1993.