Do you select the fiction and non-fiction books independently of each other (like stratification)?
I have been presented with the following question:
"On your shelf you have four books that you are planning to read in the near future. Two are fictional works, containing 212 and 379 pages, respectively, and the other two are nonfiction, with 350 and 575 pages, respectively.
(c) Suppose that you randomly select one of the two fiction books and independently randomly select one of the two nonfiction books. Obtain the sampling distribution of X for this sampling method, and determine its mean and standard deviation."
For this question i am having trouble setting up the sampling distribution. Does "independently randomly select" indicate that i am sampling WITH replacement? This doesn't seem to make sense considering i can't choose two of the same books..My thoughts were to construct a sampling distribution as such:
Fiction: 212 pages
Fiction: 379 pages
Non-Fic: 350 pages
Non-Fic: 575 pages
x1: 212, 212, 379, 379, 350, 350, 575, 575
x2: 350, 575, 350, 575, 212, 379, 212, 379
X=x: 281, 393.5, 364.5, 477, 281, 364.5, 393.5, 477
xbar: 281, 364.5, 393.5, 477
P(Xbar=xbar): 2/8, 2/8, 2/8, 2/8
My thinking here was that there are 2 fiction and 2 non fiction books; I am to select one fiction and one non-fiction. If i select the first fiction (212 pages) then i can select from either of the 2 non-fiction books. If i select the second fiction (379 pages) then i can select from either of the 2 non-fiction books again. Same principle if i pick one of the Non-Fiction books first.
Am i missing some essential point here? Any hints would be greatly appreciated!
We didn't cover the term "stratification" in class so i'm not sure if this is the correct procedure, but it does state that the fiction and non-fiction books are independently randomly selected from the lot of four books.
I omitted this as it was from parts a) and b), but X denotes the sample mean number of pages for the two books selected.
Stratification means that you sample from each strata (group) independently. If you had 2 strata, then you would have two sampling distributions: one for each strata.
You need to specify whether its with or without replacement: with replacement means that if you select something, you put it back in the population for the next sampling procedure.
If you didn't have replacement then you would only have 2 possibilities for 2 books in each strata.