Download Advanced Placement - Never Tell Me The Odds

Advanced Placement
Statistics and Probability
Name:________________________
Chapter 10
_______________________ is a method of drawing a conclusion about a certain
population derived from a sample. Several assumptions are made about the sample and they are
that the sample is _____________________, ________________________, and the sample was
obtained by a ____________________________.
Estimating with Confidence
As a sample is obtained, the sample mean should start to get closer to the true population
mean. This idea is a product of ______________________________ numbers. As we collect
more samples from the same population and find the averages for those samples, the standard
deviation of the sample means is now the population _______________________________
divided by the __________________. Once the sample means have been calculated we can make
a prediction for the ________________ mean.
We will first make a prediction with some level of confidence. If we obtain a sample
from a population and have calculated the sample mean we can make some prediction for the
population mean. Suppose we obtain a sample mean equal to 415. A 95% confidence interval
produces the numbers ______________ and ____________ with a margin of error equal to 22.3.
To say that ______________ and _____________ is a 95% confidence interval for the population
means that ______________ of the repeated ___________ trials will capture the
______________________ mean. Our sample mean is the estimate, and the margin of error is
what we ___________ and ______________ to our estimate to get our interval.
There are two conditions that must be met in order to predict the population mean based
upon the sample. Number one is ________________________________________ and the
second one is _____________________________________________________. Some of the
more common confidence intervals have z-scores related to the error allowed. The 90%, 95%,
and the 99% confidence level have corresponding z-scores which are _________, ___________,
and ___________ respectfully. In my notes I have denoted that z* in the book is the same as
_________ in my equation, where _______ is the amount of error allowed. The reason we divide
________ by two is because
____________________________________________________________________. Once you
have obtained a sample that meets the two conditions then we can use the formula
___________________ or my formula __________________ to create the confidence interval. If
your sample size increases then the M.E., which stands for __________________________, will
_________________. This again is a product of the ___________________________________
numbers. Therefore when the sample size increases the intervals will start to
_____________________________________. When all the calculations have been made and the
intervals found then our conclusion about the population mean is that
__________________________________________
_____________________________________________________________________.
Remember that in our conclusion, our opinions should not be noted in conclusion, unless it is
asked.
There are three things that will make the ME get smaller and they are ________
__________________, ________________________, and _____________________. We can
always find out how many items we need in a sample to estimate the population mean. The
______________________________ is equal to z* times the standard deviation divided by the
square root of n. Therefore we are solving for n given a certain margin of error. There are some
cautions in confidence intervals. The data must be a ____________ from the population. If the
data produced is biased then _____________ formulas will not save the data. If there are
_______________ in your data, it may influence your sample mean. The sample size may be
______________ and if the population is not normal then errors could be produced. If ______ is
bigger than or equal to ______ then the confidence level is not greatly disturbed by the nonnormal population. We must know ______. If the sample size is large enough then we can use
the sample ________________ instead of _______.
Test of Significance
The idea behind the test of significance is to assess the ____________ provided by the
data about a claim made concerning the population. In testing for significance a
_________________________ is set up which is usually a claim that is to be tested. The
_________________________ is usually what we suspect to happen in the data collected. Once
the data is collected then the data is compared to the claim. A number is assigned to our sample
mean to tell us how unlikely our observation would be if the _________________ is true. The
larger the z-score, the stronger the evidence is ____________ the
______________________________. We usually measure the strength of the evidence by the
________________. This probability is the likelihood that our sample should produce its results.
Again, when we collect data we must make sure that the data is __________________________,
________________________, and was obtained by a _________________________________.
Conducting a test for the population mean, you must do the following:
1.
_________________________________________________
2.
_________________________________________________
3.
_________________________________________________
4.
_________________________________________________
We should never ___________________ the null hypothesis. We must say that we have
sufficient ____________________. We should also never say that we _______________ the
alternative hypothesis if there is significant ________________________.
The p-value for a two-sided test is found by ________ both sides of the normal
distribution that falls into error. Testing against a fixed level of significance is comparing the
___________ vs. ______________. If your _____________ is lower than the ______ then we
have sufficient evidence against the null hypothesis. Another method of testing the mean is by
using the confidence interval. If the ____________ falls outside the confidence interval produced
by data, then there is ______________________ evidence against the
_________________________.
Making Sense of Statistical Significance
Setting a level of significance is deciding how much information is required to have
sufficient evidence to _________________ the null hypothesis. If you want strong evidence then
__________ needs to be small. In addition to attempting to gather evidence to ____________ the
null hypothesis there may be consequences to rejecting the ______________________.
Statistical significance doesn’t mean that it is _______________ significant. The sample
obtained must still be __________________, _____________________________, and generated
by _______________________.
Inference as Decision
A Type I error occurs when we ________________ the null hypothesis and it turns out
to be _________________. A Type II error occurs when we ________________ the null
hypothesis and it turns out to be ________________. _______ is assigned to a Type I error
which is called the significance level for a Type I error. To produce a Type II error you must
____________ the null hypothesis. Once you have stated the null and alternative hypothesis you
must find the corresponding sample mean value that will create a ______________ error. As
soon as you find this value, you then compare it to what the alternative believes to be true. From
there you find a z-score related to the sample mean value necessary to create a Type I error to the
alternative hypothesis.
The probability that a fixed level alpha significance test will reject the null hypothesis,
when a particular alternative value of the parameter is called the power of the test against the
alternative. The power of a test against any alternative is _____________
_______________________________________. In order to find the power of the test you must
complete the following steps:
1.
__________________________________________________
2.
__________________________________________________
3.
__________________________________________________
In order to increase the power of a test you can do several things. You can ______________
alpha, consider a an alternative ____________________________, increase the
___________________, and decrease the ________________________________.
If we do not have sufficient evidence to reject the null hypothesis, we cannot
____________ the null hypothesis. We can only say that we do not have __________________
against the null hypothesis. When testing the hypothesis you must:
1.
__________________________________________________
2.
__________________________________________________
3.
__________________________________________________
4.
__________________________________________________