Transcript Chapter 9 concept review - Somerset Independent Schools

AP Statistics –
Chapter 9 Test
Review
I can interpret P-values in context.
• QUESTION: When we are testing hypotheses,
what would be strong evidence against the
null hypothesis (𝐇𝐎 )?
• ANSWER: Obtaining data that shows a very
small p-value. (in comparison to the stated
‘alpha’ level … which is usually going to be
0.05)
I can interpret a Type I error and a Type II error
in context, and give the consequences of each.
• A Type I Error is:
– When we REJECT the null hypothesis, when the
null hypothesis, is in fact TRUE.
• A Type II Error is:
– When we FAIL TO REJECT the null hypothesis,
when the null hypothesis is in fact FALSE.
I can understand the relationship between the
significance level of a test, P(Type II error), and power.
• The probability of committing a TYPE I ERROR
is:
– Whatever, your value for α is (your significance
level, whatever it is stated to be; DEFAULT level =
0.05 (5%))
• The probability of committing a TYPE II
ERROR is:
–β
I can interpret a Type I error and a Type II error
in context, and give the consequences of each.
• What is POWER?
– It is your ability to correctly identify a FALSE null
hypothesis (Ho). (probability of correctly rejecting
a FALSE null hypothesis)
• What are some ways to INCREASE the power
of a test?
– Increase sample size ‘n’…. While keeping
significance level the same…
– Increase significance level α…. Which also means
increasing the risk of making a Type I Error…
I can check conditions for carrying out a test
about a population proportion.
• What are the assumptions for 1 prop z test
– RANDOM?
• Sample must be random….
• No VRS’s or Convenience samples
– NORMAL?
• Confidence Intervals:
– 𝑛 ∗ 𝑝 ≥ 10; 𝑛 ∗ 𝑞 ≥ 10
• Significance Tests:
– 𝑛 ∗ 𝑝 ≥ 10; 𝑛 ∗ 𝑞 ≥ 10
– INDEPENDENT?
• AKA: 10% Rule
– “We are sampling without replacement…. So population must
be 10 times larger than the sample.”
I can check conditions for carrying out a test
about a population mean.
• What are the assumptions for 1 sample t test
– RANDOM?
• Same for 1 prop z test
– NORMAL?
• We must consider the sample size and whether it is large enough.
We prefer it to be greater than 30. This is especially important if we
don’t know if the POPULATION is NORMAL or not. The Central Limit
Theorem is what allows us to assume normality AS LONG AS THE
SAMPLE SIZE IS GREATER THAN 30…
• Additionally, if the sample size is LESS THAN 30, we must look at the
data graphically and determine if there is strong skew ness or the
presence of outliers, which can cause us to doubt the normality of
the data.
– INDEPENDENT?
• Same for 1 prop z test
I can describe the sampling distribution for
proportions or means.
•
When we describe a sampling distribution, we must ALWAYS address THREE things:
– CENTER
• This is either ‘p’ or ‘μ’. Whatever they say these values are, are to be the values you
use to describe the CENTER. (Note: in most instances, we call the center “Mean”,
whether it is a proportion or not.)
• Do NOT us the p-hat or x-bar (statistics) values in place of the parameter values…!!!!
– SPREAD
• This is standard deviation.
– Proportions:
– Means:
𝒑𝒒
𝒏
𝒔𝒙
𝒏
– SHAPE
• If the sample size is GREATER than 30, then we can say it is ‘approximately normal.’
• If the sample size is LESS than 30, we can only say its ‘approximately normal’ as long as
there are no outliers or strong skew ness in the sample data.
I can check conditions for carrying out a test
about a population mean OR proportion.
• Suppose, you are testing the NORMAL condition
for a test of either MEANS or PROPORTIONS. If
your sample data, had a box plot, that looked like
this, how would you react?
• If the sample size was 100?
– It would be safe to assume normality (n > 30)
• If the sample size was 22?
– It would NOT safe to assume normality because….
(n < 30)
I can recognize when a confidence interval is
not needed for estimations.
• QUESTION: If you are able to obtain data from a
population through a CENSUS, rather than
through a SAMPLE, when would it be appropriate
to make estimations via CONFIDENCE INTERVALS
or decisions via SIGNIFICANCE TESTING?
– ANSWER:
• NEVER… if you have 100% of the data from the ENTIRE
population, then what are you estimating or trying to
decide???? (i.e.: You already know the PARAMETER values…
so, don’t bother with carrying out a test or constructing an
interval).
I can recognize paired data and use one-sample t
procedures to perform significance tests for such data.
• When we are doing a hypothesis test for
PAIRED DATA…
– What type of Test do we do for paired data and
what is the parameter of interest?
• TYPE OF TEST: 1 sample t-test
• PARAMETER OF INTEREST: The mean difference μ𝑫
– What will the null hypothesis look like?
• MEANS: 𝑯𝒐 : 𝝁 = 𝟎
I can interpret P-values in context.
• Suppose I obtain a p-value that is 0.068
• Is this significant at?
– 10% level (0.10)?
• YES
– 5% level (0.05)?
• NO
– 1% level (0.01)?
• NO
Test will consist of:
• 16 Multiple Choice Questions
• 2 Free Response Question
– Some students will get a 1 PROP Z-TEST, others
will get a 1 SAMPLE T TEST
BASELINE TOPIC(S):
• Must get AT LEAST ¾ on the FRQ
• MULTIPLE CHOICE TOPIC(s):
– MUST know how to calculate DEGREES OF
FREEDOM in order to find a ‘t’ test statistic
– MUST know the definition of Type II Error
– MUST know how to read a situation and correctly
state the NULL & ALTERNATIVE hypotheses for a
mean or a proportion.