Problem 1Throughout the 1990 s the average household expenditure on scratch tickets in a state has been $5. In 2010 a sample of 7 households was selected at random and the following expenditures for a given week were reported:$3 $2 $4 $3 $5 $4 $7(a) What is the sample mean expenditure for scratch tickets?(b) What is the sample standard deviation for the sample results?(c) What are the null and alternate hypotheses if we wished to test the hypothesis that the average expenditure on scratch tickets has decreased in the 21stcentury?(d) What is the critical score which will determine your conclusion?(e) What is the computed score found from the sample data and what is your conclusion based on these results?Problem 2A store wishes to predict net profit as a function of sales for the next year. The following table gives the years 1998 to 2005.YearSales(thousands of dollars)Net Profit1998488.01999529.420005311.32001788.62002806.62003704.1200462?1.0200555?2.0(a) Graph the points from 1998 through 2005 on a scatter diagram using Sales as the independent variable and Net Profit as the dependent variable.(b) Draw the regression line on the graph you constructed in Part (a).(c) What is the value of the coefficient of determination for this regression model? Comment on the strength of the regression line for this model.(d) What is the predicted net profit for 2006 if sales are expected to be 75?Problem 3The following table shows the last six years average new weekly unemployment insurance claims.YearAverage weekly new unemployment insurance claims200434130020053336002006311300200732120020084158002009567600(a) Forecast the new weekly unemployment insurance claims for all years from 2007 to 2010. Use a three-year weighted moving average with weights of 0.6 0.3 and 0.1. Use the largest weight with the most recent data.(b) Forecast the new weekly unemployment insurance claims using exponential smoothing with alpha = 0.6 for all years from 2005 to 2010. Use the rate for 2004 as the starting forecast for 2004.(c) Which of the methods in parts (a) and (b) produces better forecasts for the three years from 2007 to 2009? Answer on the basis of mean square error (MSE).Problem 4A financial services firm is opening a branch and they need to make staffing decisions. Administrative assistants are worth $100 in weekly profit but they require $100 from the technology budget and 50 ft2of office space. Attorneys bring in $2000 a week in profit while using $100 from the technology budget and 400 ft2of office space. Analysts are worth $500 a week in profit and use $1000 from the technology budget and 100 ft2of office space. Finally the traders are worth $1500 a week in profit but require $200 from the technology budget and 400 ft2of space. The office needs to have at least 4 administrative assistants and 10 analysts. There are only 4 attorneys available for the new office and you can bring at most 50 people to the new branch. The technology budget is $20000 per week and the new office has 12000 ft2of space available. Give the LP Model and Excel Solver to find the optimal solution.Problem 5A company purchases its merchandise for $10 and sells for each item for $20. The pay-off table for the problem is given below.Demand for ItemAlternativeLowMediumHighDo nothing000Order Low300003000030000Order Medium100005000040000Order High-100004000080000Probability0.30.30.4What is the decision based on each of the following criteria?(a) EMV approach
