The Central Limit Theorem and Sampling Distributions

Standards: IIID 1, 2, and 3
Why is the Central Limit Theorem so important, even when the distribution of x is not Normal?

Key understandings:
When does the CLT "kick in?"
Why is the standard deviation of the sample averages smaller than the standard deviation of the population?
How do you apply the CLT to compute probabilities related to the sample average?
What does sample size have to do with your certainty about the distribution?
How do these methods apply to sample proportions?

Stay on top of the material by reading the chapter and taking notes on the key concepts. Work problems. We will test on Thursday, January 21st.


Here's a version of the sampling program that works!

-> means "store"
Lbl, For, IF, End, and Goto are all programming words, so they are found under the programming menu. Just hit PRGM for access to the menu.
DON'T TRY TO PROGRAM THE ITALICIZED EXPLANATIONS


:1 -> C *Initializes the value of C, the counter
:rand(150) -> L1 *Puts 150 uniform random numbers in L1
:Lbl 10 *Labels this line for use later
:0 -> B *Resets the value of B, the partial sum of the numbers, to be 0:rand(150) -> L2 *Puts 150 more random numbers in L2
:SortA(L2,L1) *Sorts your original numbers by the second column:For(J,1,10):L1(J)+B -> B: End *Takes the top 10 numbers, and adds them together
:(B/10) -> L3(C) *Calculates the average and puts it in the next row of L3:C + 1 -> C *Changes the counter to the next number
:If C < 101: Goto 10: *Starts over to select another sample of 10 from the population



Please answer these questions every time you work a problem that requires a calculation.

What is the population of interest?
What is the sample?
How can you justify using the Normal distribution?
Why are you allowed to use that simplified standard deviation?
Is your sample large enough?
Is your sample an insignificant part of the population?
Was your sample selected randomly?
Are the observations independent?

What is the distribution of the sample statistic?
Have you drawn the normal distribution graph and labeled it?
Have you shaded the appropriate part of the graph?
Have you checked your answer to see if it looks reasonable?

Work a bunch of problems from the text. Cici's 2-4 Sunday. Test Thursday.