II. Show work so partial credit may be given. Answers are to be placed on the template and submitted through the View/Complete link. (8 points) Short Answer Question 1 As a purchasing manager, you are assessing the delivery time of two potential package delivery companies to your facilities overseas. Federal Express has delivery time that is normally distributed with population mean = 34 hours with population standard deviation = 3 hours while DHL has delivery time that is normally distributed with population mean = 36 hours with population standard deviation = 5 hours. Your maximum desired delivery time is 32 hours. a) There is a 65% probability that delivery time with DHL will be greater than what amount of hours (include 2 decimals)? b) You will evaluate the delivery companies based on their likelihood of meeting your maximum desired delivery time. Which supplier is expected to have a smaller likelihood of meeting your maximum desired delivery time of 32 hours (justify your response)? (9 points) Short Answer Question 2 The Marriott Hotel marketing team wants to estimate , the proportion of the hotel guests who were return visitors in the past three years. They select a simple random sample of 150 guests from the past three year's records and finds that 27 of the sampled guests are return visitors. a) Compute a point estimate for . b) What are the upper and lower bounds for the 90% confidence interval for (4 decimals)? c) Marriott has decided to offer a room discount for returning visitors unless the sample provides evidence (with 90% confidence) that is greater than 0.15. In that case, Marriott will not offer the discount. State the null and alternative hypotheses (in symbols) that need to be tested in order to make the decision. d) Based on the confidence interval in part b, would you conclude that the Marriott should offer the room discount? (Justify your response). (26 points) Short Answer Question 3 Universal Studios is developing a model to predict first week number of tickets sold to its non-animated movies. Universal collects information on 17 recent releases and wants to identify those characteristics that are related to TICKETS. TICKETS Number of tickets sold in the first week (in millions of tickets) COST Production plus marketing cost (in millions of dollars) THEATRE Number of theatres (in hundreds of theatres) HOLIDAY = 1 if the movie opened on a holiday weekend DRAMA = 1 if the movie is a dramatic movie (ex. Twilight Saga) ACTION = 1 if the movie is an action adventure movie (ex. Pirates of the Caribbean SUPERHERO = 1 if the movie is a superhero movie (ex. Spiderman) CMO =1 if the movie is a comedy/musical other movie (excluded category) The data was used to fit the following three models in which the dependent variable is TICKETS MODEL 1: Multiple Regression for tickets Multiple Adjusted StErr of R-Square Summary R-Square R 0.8973 Estimate 0.8051 0.7922 3.3093 Sum of Squares Mean of Squares F---Ratio Degrees of ANOVA Table Freedom 1 15 Explained Unexplained 678.7886 164.2702 Coefficient t---Value p---Value 3.9855 0.0944 1.8490 7.8729 0.0843 0.0000 p---Value 678.7886 10.9513 Standard Error Confidence Interval 95% Lower Upper Regression Table Constant cost 2.1556 0.0120 8.5800 0.0689 0.6089 0.1200 MODEL 2: Multiple Regression for tickets Multiple Adjusted StErr of Estimate R---Square Summary R R---Square 0.9405 0.8846 0.8579 2.7362 Sum of Squares Mean of Squares F---Ratio p---Value Degrees of ANOVA Table Explained Unexplained Freedom 3 13 745.7338 97.3251 248.5779 7.4865 Coefficient Standard Error t---Value p---Value Confidence Interval 95% Lower Upper 2.1404 0.0491 2.0814 0.0181 1.0284 2.7071 0.3225 0.0180 1.6813 3.3123 0.7985 2.1165 2.1056 1.5650 0.0552 0.1416 6.6369 0.0099 value 1.2602 Regression Table Constant cost theatre holiday 2.3561 0.0883 suppressed 7.8848 MODEL 3: Multiple Regression for tickets Summary Multiple R-Square R Adjusted StErr of R-Square Estimate 2.6654 0.9569 0.9157 0.8652 Degrees of Sum of Mean of ANOVA Table Freedom Squares Squares Explained 6 10 772.0149 71.0439 F---Ratio Unexplained 128.6691 7.1044 p---Value Standard Coefficient Regression Table Constant cost theatre holiday drama action superhero Confidence Interval 95% t---Value p---Value Error 4.9852 0.0513 1.7970 4.1837 0.8494 2.7367 0.0201 0.8259 2.1604 2.3351 1.8216 value 2.1758 1.9365 0.3637 0.0985 suppressed 0.0546 0.0816 0.7236 2.3487 3.6062 2.0283 1.9935 1.1580 1.8090 0.2738 0.1006 Lower Upper 11.0829 0.0066 0.0432 0.6301 4.3535 2.1705 0.8355 1.1124 0.0961 3.6371 8.9974 a) What is the value of the simple correlation between TICKETS and COST? b). If you are able to determine the answer, is showing the film in more theatres associated with higher ticket sales (with cost and holiday opening held constant) with = 0.05? (Justify your response). c) If you are able to determine the answer, do higher cost movies have higher ticket sales (with THEATRE, HOLIDAY and movie genre held constant) with = 0.05? (Justify your response). d) If you are able to determine the answer, do movies opening on holiday weekends have different ticket sales than those opening on non-holiday weekends (with COST held constant) with = 0.05? (Justify your response). e) Interpret the coefficient for COST in Model 1 (that is, interpret the estimated value of 0.0944 without considering whether or not this value is \"statistically significant\"). f) Interpret the coefficient for ACTION in Model 3 (that is, interpret the estimated value of 2.3487 without considering whether or not this value is \"statistically significant\"). g) Interpret the coefficient for THEATRE in Model 2 (that is, interpret the estimated value of 1.6813 without considering whether or not this value is \"statistically significant\"). h) Which model would you recommend to predict TICKETS with = 0.05? (Justify your response). i) Based on model 3, predict TICKETS for a superhero movie opening in 3500 theatres on a holiday weekend that cost $150,000,000. Use all variables in Model 3 to obtain your prediction even if some of them are not \"statistically significant\". j) What is the 95% prediction interval for your prediction in part i)? 6.0522 6.8679 8.0479 (7 points) Short Answer Question 4 You are a real estate developer and are trying to determine the EMV of your net commission from a sales call to a potential purchaser. Assume that your transportation cost is $1.45 per mile Assume that the sales call is 70 miles round trip Assume that your transportation time is 2.25 minutes per mile Assume that the value of your time for transportation is $55.00 per hour Assume that it will take 3 hours to meet with the potential purchaser Assume that the value of your time for the customer meeting is $150.00 per hour Assume that you will have a 19% chance of a successful sales call (sales call #1) If sales call #1 is successful, you will sell a house valued at $275,000 with likelihood = 55% you will sell a house valued at $300,000 with likelihood = 35% you will sell a house valued at $425,000 with likelihood = 10% Assume that your commission will be 2.5% of the value of the house if sales call #1 is successful. a) What is the expected cost (time and transportation) of sales call #1? b) Without assuming that the sales call will be successful (that is, it may or may not be a success), what is the expected gross commission of sales call #1 (do not net out the expected costs)? Suppose you have a second possible sales call (sales call #2). Assume that the expected cost remains the same and that the commission rate remains 2.5%, but that the following information is the different information for sales call #2. Assume that you will have a 12% chance of a successful sales call (sales call #2) If sales call #2 is successful, you will sell a house valued at $285,000 with likelihood = 45% you will sell a house valued at $320,000 with likelihood = 25% you will sell a house valued at $355,000 with likelihood = 30% c) Assuming that your sales call is successful, which sales call is the maximin sales call? (Don't simply define maximin, but use values to justify your response)