Unformatted text preview: variables
With quantitative variables, we are now
looking at means
Instead of the proportion of ILRies (Cornell’s
sexiest major) in the class, think about the
mean number of ILRies (Cornell’s sexiest
major) in the class
Still can use the normal model! Check assumptions and conditions
State the parameters and the sampling
distribution model
Make a picture by sketching the model and
shading the area we’re interested in
Use the standard deviation as a rule to find
the zscore of the cutoff position
Use a computer program, table or calculator
to find the resulting probability, then
interpret it in context of the question The fundamental theorem of statistics!
Explaining the CLT
◦ The sampling distribution of any mean becomes
more nearly Normal as the sample size grows. All
we need is for the observations to be independent
and collected with randomization. We don’t even
care about the shape of the population distribution! The
The CLT
◦ The mean of a random sample is a random variable
whose sampling distribution can be approximated
by a Normal model. The larger the sample, the
better the approximation will be. 2 10/30/2011 Same assumptions as modeling proportions
◦ Independence Assumption
◦ Sample Size Assumption Think about if Independence is plausable, and
check related conditions
◦ Randomization Condition: Data values must be
sampled randomly, or concept makes no sense
◦ 10% Condition n no more than 10% of population if
Condition:
drawing without replacement
◦ Large Enough Sample Condition Think about
Condition:
sample size in the context of the population Think about the assumptions and check the
conditions
State the parameters and the sampling model
Make a picture
Use the standard deviation as a ruler to find
the zscore and cutoff
Use computer program to find probability and
interpret result in proper context A confidence interval for a proportion tells us
about the sampling distribution of the sample
proportion
If we don’t know p, we use what we do know
(phat)
◦ Whenever we estimate the standard deviation of a
sampling distribution, we call it a sampling error We know that for 95% of random samples, phat will be no more than 2 SEs away from p
Don’t know true value, but can compute an
interval that probably contains the true value When a random sample is drawn from any
population with mean mu and standard
deviation sigma, its sample mean, ybar, ha...
View
Full Document
 Spring '14
 Normal Distribution, Standard Deviation, Statistical hypothesis testing

Click to edit the document details