Download Advanced Placement

Advanced Placement
Statistics and Probability
Name:__________________________
Chapter 11
Inference for the Mean of a Population
In the previous chapter we made an unrealistic assumption that we knew the value
of ____________. In reality the ______________ is unknown and in this chapter we will
proceed with out knowing the population ________________. There are some
conditions that need to be set concerning the inference about the mean. The first one is
that the sample needs to be obtained by a __________. This is a very important
condition that needs to be met. The second condition is that observations from a given
population need to be _______________. Since we do not know the population
_______________ we must change our standard deviation. Now we use the formula
_______________ to find the standard error of the sample ____________.
In the previous chapter we knew the standard deviation, but now we use
____________ instead of the population standard deviation divided by the square root of
n. The result of this substitution is that now our distribution will not be _____________.
In stead of using a normal distribution (z-distribution) we will now use the
___________________. Since we no longer have a normal distribution, the z-score
formula will not work. We must use the one sample ________________ which is equal
to the formula _______________________. This formula uses the idea that we have
_______________ degrees of freedom. As you look in the book, the graph on page 618
has something interesting going on. As the degrees of ____________ increase, the curve
starts to approach the ____________________ distribution. Now turn to table C (the
back of the book). You will notice that as the degrees of ___________ increase the tscore starts to approach the _______________ when n is really large.
Our first inference, just like in the previous chapter, will be confidence intervals.
The formula doesn’t change that much. The original formula, _________________ will
now become __________________. There are two major differences with the new
formula for finding the confidence interval. The first is the replacement of the z*. The
z* has been replaced with the ___________. This _________ is similar to the z of alpha
divided by two (my equation). You now must refer to Table _____ to find all the
appropriate t-scores. When looking up a certain t-score, the numbers at the top of the
table represent _________________ and the numbers at the side represent
_______________________. It is important to know the sample size, or the
______________________ cannot be found, which is needed to find the corresponding tscore. The second major change to the formula is the ___________________. Instead of
using the population ________________, which we no longer are given, we must use
______________________. To test the hypothesis, nothing has changed that much. The
null and _______________ hypothesis are still stated. The only major difference is the
________________ which is now __________________. When conducting a test there
are important steps that one must take…(see example 11.2)
1.
_________________________________________________
2.
_________________________________________________

you should check to see if your sample is _______________ by using
the ______________ probability plot. It should be in a
__________________.
3.
_________________________________________________
4.
_________________________________________________
These steps are very important. One thing you must pay attention to is that you must
never ever _______________ the null or alternative hypothesis. Rejecting a hypothesis
is okay, but you must have _______________________ evidence.
Finding the p-value for a t-score is a little harder than using the normal
distribution table. You can estimate it by finding where your _____________ lies. If it is
between two t-scores, you can get a rough idea for the ____________. Your calculators
have the ability to find the actual ____________ by using the ONE-SAMPLE
_________________.
Under a match pair design you are comparing the differences between two items.
The null hypothesis for this type of test is always going to be equal to ____________.
Thus we are saying that the ______________ between the two items will be _________.
When conducting a hypothesis test for match pair be sure to follow all ________steps.
The formula used in this test is basically the same as a t-test, but mu will be equal to
_________. When finding the confidence interval for a match pair, the result will be the
_________________ between the two items. Thus the interval contains the true
______________ with some level of confidence.
The significance test is considered ___________ if the confidence level or pvalue is not changed even if we assume the procedure is _______________. Unlike the
previous chapter, all variables such as the sample mean, standard deviation, and the tscores is highly influenced by ___________________. Due to this we have set some
parameters to go by based upon the sample size. The t procedures are…
1.
___________________________________________________
2.
___________________________________________________
3.
___________________________________________________
4.
___________________________________________________
So, if you have a large sample that contains ___________________ the t-procedures
could be used.
In practice we hope to show that the null hypothesis is _____________. So, a
_____________ power is very important. When conducting a test to disprove the null
hypothesis we assume that the fixed level of alpha to be _______________. Finding the
power of a test is just like the previous chapter, except now we use a ________________
and the ___________________ in the formula. Remember that power is equal to
______________________.
Comparing Two Means
We are now going to compare two different populations by obtaining two
____________________ from each population. Remember that each sample obtained is
____________________, ______________________, and has been produced by a
______________________. The conditions for comparing the two different populations
are that…
1.
___________________________________________________
2.
___________________________________________________
When we actually do a hypothesis test, we will always set the null hypothesis to be
__________________________________. The alternative has three possible outcomes
and they are _______________, ________________ or ________________.
Before we get into the actual test, we need to discuss the sampling distribution of
difference of the two means. The mean of the difference of the two sample means is
equal to _______________________. That is the difference of the sample means is and
____________________ estimator for _______________________________________.
The variance is a bit different than before. Now the variance will be ________________
if the population standard deviation is known. The SE, which stands for
_____________________________________________, of the sampling distribution
where the standard deviation is unknown will be ________________________________.
This will then give us the new t-score formula with is…
________________________________
If the standard deviation for the population is known, then we use….
________________________________
There are two options when dealing with the degrees of freedom. The TI 83/89 or other
graphing calculators automatically calculate the ___________________ based upon the
data. If a calculator is not available and tables are the only things a student has to rely
upon then the degree of freedom is equal to ________________ of the _____________
or _________________.
Now that we have the SE, we can actually test a hypothesis about the differences
between two populations or even calculate a confidence interval concerning the
______________ between two populations. The new equation for confidence interval
with an unknown standard deviation is…
_________________________________
where the degree of freedom is found by using the _____________ of ___________ or
_____________. If you have a confidence interval concerning the difference and the
interval covers 0 then you cannot __________________ any ___________________
concerning the difference between the two populations. (see example 11.12).
The robustness of the two sample t-test depends on more than one sample. So, for
the sake of the values given on page 636 we will use the _____________ of the two
samples instead of using one sample. Remember to check the normality of your sample
one at a time. To check for normality you can use the __________________ and check
to see if it is ________________________.
The formula for the degrees of freedom for a two sample t-statistics is already in
the calculators. The formula is…
___________________________________ only when n is __________ or larger. This
value is the actual ______________. The method used when a calculator is not available
nor is this equation is to ___________________________________________________.