The average stopping distances for a population of school buses traveling 50 miles per hour, measured in feet, are normally distributed, with a standard deviation of 6 feet. Using a random sample of 23 buses having a sample mean of 262 feet, construct a 95% confidence interval for the mean stopping distance of the population.

Suppose you sample 19 high school baseball pitchers and find that they have an average pitching speed of 87 miles per hour with a standard deviation of 0.98 mph. Find a 95% confidence interval for the average pitching speed of all high school baseball pitchers. Assume that the population is normally distributed.

A fisherman can row upstream at 4mph and downstream at 6mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. How far did the fisherman row if the entire trip too 6 hours?

The distance the fisherman rowed in ----- miles
     (Type an integer or a decimal)

We know how difficult it is to find a convincing instrumental variable Zi to overcome the “unobserved ability” problem in a wage regression to measure the returns to education. Critically discuss whether Zi =”distance in miles of high school location of workeri to closest four year college”satisfies the two properties of a valid instrument.

Donna Shader, manager at the Winter Park Hotel, is considering how to restructure the front desk to reach an optmum level of staff efficiency and guest service. Presently, the hotel has five clerks on duty, each with a separate waiting line, during the peak check in time of 3:00 P.M to 5:00 P.M.

Observation of arrivals during this time show that an average of 90 guests arrive each hour (although there is no upward limit on the number that could arrive at any given time). It takes an average of 3 minutes for the front-desk clerk to register each guest.

Donna is considering three plans for improving guest service by reducing the length of time guests spend waiting in line.

The first proposal would designate on employee as a quick service clerk for guests registering under corporate accounts, a market segment that fills about 30% of all occupied rooms. Because corporate guests are preregistered, their registration takes just 2 minutes. With these guests separated from the rest of the clientele, the average time for registering a typical guest would climb to 3.4 minutes. Under plan 1, noncorporate guests would choose any of the remaining four lines.

The second plan is to implement a single line system. All guests could form a single waiting line to be served by whichever of the five clerks became available. This option would require sufficient lobby space for what could be a substantial queue.

The third proposal using an automatic teller machine (ATM) for check-ins. This ATM would provide approximately the same service rate as a clerk would. Given that initial use of this technology might be minimal, Shader estimated that 20% of customers, primarily frequent guests, would be willing to use the machines.

(This might be a conservative estimate if the guests perceive direct benefits from using the ATM, as bank customers do. Citibank reports that 95% of its Manhattan customers use its ATMs.) Donna would set up a single queue for customers who prefer human check-in clerks. This would be served by the five clerks although Donna is hopeful that the machine will allow a reduction to four.

Required:

1. Determine the average amount of time that a guest spends checking in.
2. What is the check in time under each plan?
3. What plan would you recommend.

2. Courtney Newell, manager of the Silver Park Hotel, is considering how to restructure the front desk to improve guest service during the peak check-in hours of 3:00 to 5:00 p.m. At present, the hotel has 5 clerks on duty each with a separate waiting line.

Courtney is considering two plans for reducing the guest’s waiting time. The first proposal would be to implement a single waiting line in which guests would be served by whichever of the 5 clerks becomes available first. Observations of arrivals during the peak check-in time show that a guest arrives on average every 40 seconds. It takes an average of 3 minutes for the front-desk clerk to register each guest.

The second proposal would designate one employee as a “quick-service” clerk for guests registering under corporate accounts, a market segment that comprises about 30% of Silver Park’s guests. Since these guests would be pre-registered, it would take an average of only 0.5 minutes for the front-desk clerk to register them. Under this plan, the non-corporate guests would form a single line and proceed to the first available of the 4 remaining clerks. The average time for registering a non-corporate guest is 3.4 minutes.

Which proposal should Courtney implement? Provide appropriate quantitative evidence to support your recommendation.

1. Courtney Newell, manager of the Silver Park Hotel, is considering how to restructure the front desk to improve guest service during the peak check-in hours of 3:00 to 5:00 p.m.  At present, the hotel has 5 clerks on duty each with a separate waiting line.

Courtney is considering two plans for reducing the guest’s waiting time. The first proposal would be to implement a single waiting line in which guests would be served by whichever of the 5 clerks becomes available first.  Observations of arrivals during the peak check-in time show that a guest arrives on average every 40 seconds.  It takes an average of 3 minutes for the front-desk clerk to register each guest.

The second proposal would designate one employee as a “quick-service” clerk for guests registering under corporate accounts, a market segment that comprises about 30% of Silver Park’s guests.  Since these guests would be pre-registered, it would take an average of only 0.5 minutes for the front-desk clerk to register them.  Under this plan, the non-corporate guests would form a single line and proceed to the first available of the 4 remaining clerks.  The average time for registering a non-corporate guest is 3.4 minutes.

Which proposal should Courtney implement?  Provide appropriate quantitative evidence to support your recommendation.

P(W)= 0.3 P(low/W) = 0.50 P(low/S) = 0.10 P(S)= 0.7 P(medium/W)= 0.40 P(medium/S)= 0.25 P(high/W) = 0.10 P(high/S) = 0.65 BDSC 340.001-3 d) Construct a decision tree for this problem and analyze it. e) What is McHuffter’s optimal decision? f) What is the expected value of the survey(sample) information?

Suppose the price elasticity of demand for heating oil is 0.2 in the short run and 0.7 in the long run.

If the price of heating oil rises from $1.20 to $1.80 per gallon, the quantity of heating oil demanded will (RISE/FALL) by ____ % in the short run and by ______% in the long run. The change is (LARGER/SMALLER) in the short run because people can respond (MORE/LESS)  easily to the change in the price of heating oil.

The Fresh Detergent Case

Enterprise Industries produces Fresh, a brand of liquid detergent. In order to more effectively manage its inventory, the company would like to better predict demand for Fresh. To develop a prediction model, the company has gathered data concerning demand for Fresh over the last 33 sales periods. Each sales period is defined as one month. The variables are as follows:

Demand = Y = demand for a large size bottle of Fresh (in 100,000)

Price = the price of Fresh as offered by Ent. Industries

AIP = the average industry price

ADV = Ent. Industries Advertising Expenditure (in $100,000) to Promote Fresh in the sales period.

DIFF = AIP - Price = the "price difference" in the sales period

Question:

1. Obtain the correlation matrix for all six variables and list the variables that have strong correlation with Demand. High correlation is r > 0.50. Explain your findings in plain language.