Due 9:50AM Monday, November 15, 2004.
This is an exam. You may use your notes, your book, your assignments, the Internet, and divine guidance (if it happens to be available to you), but you may not speak to people other than your beloved statistics instructor about the content of the exam. Feel free to bring questions to class on Friday. There is no time limit for this exam.
(6 points) Suppose I define a random variable X by drawing a card from a standard 52-card deck, and recording the numerical value of the card (considering face cards to have numerical value 10). For example, X(Ace of Spades) = 1, X(Jack of Diamonds) = 10, and X(7 of Hearts) = 7.
What is the expected value of X?
What is the standard deviation of X?
(9 points) Let's pretend that a particular classical music radio station is doing a pledge drive for 10% of the year. During pledge drives, music is playing 40% of the time. When there's no pledge drive, music is playing 80% of the time.
If you tune in at a random time, what's the probability that you will hear music?
Are "music is playing" and "there's a pledge drive on" independent events? Justify your answer using the mathematical definition of independence, not a common sense definition.
If you tune in at a random time and hear music, what's the probability that there is a pledge drive going on?
(5 points) I plan to run a survey to determine what proportion of people prefers the music of Marilyn Manson to the music of Alvin and the Chipmunks. I have good reasons to expect the proportion to be somewhere between 10 and 30 percent, and I don't want to spend any more money on this poll than I have to. How many people should I survey if I want to have a 95% level of confidence and a 3% margin of error?
(12 points) I randomly selected 10 books from my office (mainly computer science and math books) and 12 books from my house (mainly literature). The mean number of pages in my office sample was 480, with a standard deviation of 216. The mean and standard deviation for the page counts from my house were 388 and 165.
Construct a 90% confidence interval for the mean number of pages in the books in my house.
Set up and execute a hypothesis test comparing the mean book lengths in my office and house.
What assumptions do you need to make about my two libraries to justify the use of the techniques you used in the previous two questions? Are these assumptions plausible?
(2 points) I forgot to write down your book suggestions after the last test. If you'd suggest a book or two (and while you're at it, a favorite movie), I promise to compile a list of all the suggestions and send them to you. Then we can all read and watch each other's favorites over break, assuming we're not sleeping the whole time.
(12 points) Do problem 10 from Chapter 26.