Question 1: The listed sample distances (in millimeters) was obtained by using a pupilometer to measure the distances between the two pupils for a bunch of adults.
67 66 59 62 63 66 66 55 63 61 60 56 66 67 59 59 60 62 61
a) Give the following information:
xbar
s
n
df
t* or z* (whichever is appropriate) for 90% confidence interval
b) Give a 90% confidence interval for the distances between pupils for the population of all adults.
c) in what ways could you minimize the MOE (if you don't know what the MOE is, use your book)
Question 2:
One of the ways we could do that is to add more people, so that's what were going to do. Here are the pupil distances of more people. (INCLUDE THESE WITH THE NUMBERS WE ALREADY USED)
63 52 57 63 60 64 65 63 64 59 60 60 60 66 56 62 60 62 56 60 60 58 52 54
a) My science book here claims that the distance between pupils is 60 mm for the average adult. We want to see if the results we just got will back up this claim.
b) Set and run either a z.test or a t.test, whichever you deem more appropriate.
c) using your results from b,explain what we know based upon our information.
Question 3:
When 70 convicted embezzlers were randomly selected, the mean length of their prison sentence was found to be 22.1 months and the sd was 8.6 months (from the US DOJ). A governor is running on a platform to be tough on crime; she claims that prison terms for convicted embezzlers on average is under 2 years. Use your knowledge to try and evaluate her claim. Use alpha=0.01 for this question.
a) Run the appropriate tests for this to come to a conclusion. Give me all necessary information.
b) What would have happened if we had used an alpha of 0.05 instead of 0.01? What would have changed?
Last Question (there's only one--a thousand pieces though, of course)
Based on a couple of different accounts, averages, etc. etc. it appears as if the average college student pays about $300 a semester for textbooks.
http://bookstore.mbsdirect.net/bennington.htm
I started to get curious as to how much the average Bennington College student theoretically payed for books per semester. I say theoretically because there are a lot of pieces here that will come into play.
This used to be really hard to figure out (and a real number still would be), but through the virtual bookstore, I believe we can come up with a reasonable approximation. NOTE: this is for books only, not materials, supplies, or any other aspects.
There are, as far as I can tell, 196 courses offered in the Bookstore. We're going to make a couple of assumptions to make our lives easier:
classes are not linked to each other. In other words, we assume the pure spirit of Bennington and believe that people are taking classes from all disciplines.
all classes are taken equally. This means we are assuming all classes are a similar size and thus each book is purchased equally
each student takes four courses, regardless of the number of credits (again, for simplification)
we will also assume that if the book is sold at the book store, that is the only place a student will buy the book
a) How are you going to handle if the bookstore if it gives you a new and a used price? Make a declaration as to how you will select a proper price for the book. (note: it will also give you a list price, which may or may not be useful)
b) how are you going to randomize for each of the students?
c) given the above constraints, outline a method for figuring out how much 10 different idealized students would spend on books (this should not require actual data from actual students).
d) set a null and alternate hypothesis for the outcome of this experiment, then follow the steps below to complete the hypothesis testing. (hint: look at the first sentence in this question)
e) get your ten values for the students. Describe the shape of this data as best you can (because there's only ten data points, it may not be accurate of the whole population). Do not throw out any values--our list is so small that we should include any problems that we might get.
f) find a 95% confidence interval for how much you believe the average student will spend on books at Bennington College.
g) what changes would you want to make to the procedure we have outlined here? Would you ask any other different questions or make any different assumptions? In a brief paragraph, explain the differences you would have compared to those set forth here.
h) In a separate e-mail labeled "quick data", send me your 10 data points, 95% confidence interval and ONE sentence outlining your position based upon the null and alternate hypothesis.
extension:
1) I will e-mail you by Saturday morning a list of everyone's data points, 95% CI and sentence position. You should take this data and write a brief paragraph comparing and contrasting any major differences in the data that people had. What were the major departures, and are there any disagreements? Explain what you think to be the TRUTH about these data and assumptions. (fairly open ended, so be complete in your analysis)
2) Instead of the way we compared the prices, it would have been possible to set the experiment up in a different way:
Select 40 classes at random
Get a sample mean and sd for all book prices at once
Give a confidence interval for each class cost
multiply by four
Set a Ho and a Ha, get a 95% confidence interval, and get the values. Use the same assumptions you did here as you did in question 3 (about new and used prices, how you randomized, etc. etc.)
How is this different than the values you and your classmates got in doing the testing the other way?
How did the values change? (specifically I'm thinking of the MOE and sd, but there may be other changes as well).
Which way do you think gives a better approximation? Think through your reasoning. Be careful to thikn through HOW the approximations were made.
3) Ask your friends how much they remember spending on books this semester. Based upon all of this information, do you think they are telling the truth?