As before, so you need not submit your Excel worksheet for math problems unless you'd like to show me your work or you'd like some feedback on how you did the problem. Feel free to just answer in your FirstClass email if you prefer.
Q1. (10 points) (question 10.2 from Freund, 7th) The manager of a sport fishing products company wants to test the null hypothesis that certain lead fishing weights have a mean weight of 4.0 ounces. Explain under what conditions the manager would commit a Type I error and under what conditions the manager would commit a Type II error.
Q2. (10 points) (adapted from question 10.10 from Freund, 7th) The average drying time of a manufacturer's paint is 20 minutes. Investigating the effectiveness of a modification in the chemical composition of the paint, the manufacturer wants to test the null hypothesis μ=20 against a suitable alternative, where μ is the mean drying time of the modified paint.
Q3. (10 points) (question 10.12 from Freund, 7th) The "reasonable and customary" fee for anesthesia services for a surgery lasting less than 1 hour in a certain region is $425, as specified by an HMO. A particular anesthesia office is suspected of charging, on average, more than this amount, and a random sample of 45 of their billings shows x-bar = $455 and $s=44. Can we conclude at the 0.05 level of significance that this particular anesthesiology office charges on average more than $425? Even if you don't show your work, you must at least give your calculated statistic and either its p-value or the critical value that allows you to make your decision.
Q4. (10 points) (question 10.18 from Freund, 7th) A police patrol car drives a prescribed route in a neighborhood, and the dispatcher wants to know whether, if uninterrupted, the average time required by the patrol car to drive its route is 28 minutes. If, in a random sample of 36 uninterrupted rounds, the police car averages 29.5 minutes, with a sample standard deviation of 6.1 minutes, can the dispatcher reject the null hypothesis μ=28 minutes at the level of significance 0.05? Please show your work for this, including the critical value and the p-value.
Q5. (10 points) (question 10.22 from Freund, 7th). In nine test jumps, a newly designed track shoe enables a high jumper to jump an average of 7.02 feet with a standard deviation of 0.24 foot. What does this tell us about the athlete's claim that with the new shoes he can jump an average of 7.1 feet? Test at the 0.05 level of significance whether his true average jump is less than 7.1 feet. Please show your work for this, including the critical value and the p-value.
Q7. (10 points) Build a variant of one of the "shortest line" queuing models (see the lecture on queuing models), where, if the line is longer than 5 people, the customer immediately exits without buying anything. (This is called "balking.") Count how many customers we lose due to balking. Make whatever other assumptions you need to make and report them.
Q10. (20 points) Build a model of a bank in which there is 1 ATM machine and 2 tellers. Some customers (20 percent) have cash to deposit and always go to the tellers; the others always go to the ATM. The arrival rate is exponential with mean 5 minutes. The cash customers have a Gaussian service time, with mean 10 minutes and standard deviation 5 minutes. The ATM customers have a service time that is uniform between 2 minutes and 6 minutes. Plot the queue length. Determine the average waiting time of a customer over 50 trials, with each run being 4 hours long. (This calculation must be over all customers, not just ATM or teller customers. Hint: use timer blocks or use a weighted average.) Do you think they should add more ATMs or more tellers? Why?
Q11. (20 points) Build a model of a simplified doctor's office. Customers arrive and wait to be seen by the nurse. The nurse takes their height, weight, blood pressure and pulse. That takes about 5 minutes (Gaussian, with standard deviation of 1 minute). After that, they wait to see the doctor. The doctor's service time is usually about 20 minutes. (Gaussian, with std. dev. of 5 minutes.) However, with 10 percent probability, the doctor takes 40 minutes (Gaussian, std. dev. of 5 minutes). Most customers come by appointment, which are scheduled 20 minutes apart, so people arrive around every 20 minutes (Gaussian, std. dev of 5 minutes). However, walk-ins arrive with an exponential rate of every 2 hours. (Use the "Combine" block (Discrete Event / Routing) to combine two sources of events.) Despite the appointments, the office uses a strict first-come, first-served policy. What is the average number of people served in an 8-hour day? (The doctor skips lunch.) Does the distribution look Gaussian?
Q12. (10 points) I'd like everyone to start thinking about the project. This will be a Extend model of your own that you'll build over the course of several weeks. It need not be any larger than our other Extend models, but it may require a bit more thought and research, as you determine suitable distributions, equations and so forth. Towards that end, I'd like you to list three ideas you are considering. You don't have to make any commitment at this point, but each idea:
So that I can keep submissions straight, it would be helpful if you would name your documents with your initials at the beginning. Putting your Excel stuff all in one document, using different worksheets, is more convenient for both of us. For example, I might turn in the following:
sa-hwk7.xls sa-balking.mox sa-bank.mox sa-doctor-office.mox
I don't care that much what you call the files, but prefixing your initials means that they all fall together in my directory and I can see at a glance that you've turned everything in and I can easily launch them.
Attach the items to an email message and send it to CS199-F04-drop. Check that folder to be sure that your message is in there. Please answer text questions in the email message, rather than attaching a MS Word document.
You may work with another person on these problems, but in a limited way. I think that we can learn a lot from one another, but I also think that we learn a lot from the individual struggle to recall, synthesize, and create. Help from another student can inadvertently hinder that necessary struggle.
The rule is that you are encouraged to talk with one another at an abstract, conceptual level, not at the level of Excel formulas, Extend models, and other stuff that you would turn in. Of course, you may help one another with "reminders," such as "what was the name of that Excel function?" A good rule of thumb is that if you would feel comfortable asking me the question, you may certainly ask one another.