Transcript - MBHS Statistics

From Statistics to the Real World
Avoiding Common Mistakes
Rebecca Graber
AP Statistics pd. 3
Sampling Distribution Models
Fiction:
• Sampling distribution is
the same as the
distribution of a sample
• If you increase the sample
size, each sample will
become more normal
Reality:
• The sampling distribution
is based on an infinite
number of samples, not
just one
• If you increase the sample
size, each sample will
look more like the actual
population
Confidence Intervals Are Not:
• Probabilities (p is definitely established, we just don’t know
what it is)
•Distributions (all values are equally likely)
•Definite intervals (they are one of an infinite number of
confidence intervals, derived from different samples)
EX:
Wrong: “There is a 97% probability there is an elephant in my
room”
Right: “I am 97% confident there is an elephant in my room”
Hypothesis Testing
• Red flags (conceptual):
– “I accept Ho” : this is not
an option, you either reject
or fail to reject
– No mention of P-value: the
P-value is the entire point of
the test
– No given alpha: you can’t
accept or reject an Ho
without some sort of
threshold, it must be
decided BEFORE you do
the test
– Failure to check conditions
• Red flags (numerical)
– Number of predicted
failures < 10
– Forgetting to multiply
P by 2 for a two-tailed
test
– Using sample data for
the SD
– Having a c.i. that
includes Ho
Hypothesis Test Ex (errors in
red)
Situation: Five years ago, 40% of all living rooms in the U.S. had an elephant hidden under the
couch. Recently, a researcher looked through 20 houses in one neighborhood, and found 10
elephants. Has the proportion changed?
Test:
Ho: p = .4
Ha: p  .4
(Alpha?)
Conditions:
20 < 10% of all houses in the U.S.
10 successes, 10 failures both > 10
Random, independent sample
One proportion z-test:
SD= (.5*.5/20)^½ = .112
P-value = P(z > .1/.112) = .19
I accept Ho, so I think p=.4 (p-value? Significance?)
Errors and Power of a Test
• Type I errors are always more serious (T/F)
• Type II errors are always more serious (T/F)
• The power of a test refers to the ability to detect
any kind of error (T/F)
• We want to maximize beta (T/F)
• When looking for a Type II error, our guess of
the true p is Ha (T/F)
Errors and Power of a Test
• Type I errors are always more serious (T/F)
• Type II errors are always more serious (T/ F)
• The power of a test refers to the ability to detect
any kind of error (T/ F)
• We want to maximize beta (T/ F)
• When looking for a Type II error, our guess of
the true p is Ha (T/ F)
Which is more serious?
• Situation 1: Conducting a test to see if there is an
elephant in the room. If I think there is one, I will
have to pay $3,000 for elephant removal services
to come. If the elephant is not removed, it will
leave a nasty imprint on my floor.
• Situation 2: Conducting the same test. If I think
there is an elephant, I will pay $20 for it to be
removed. If the elephant remains in my living
room for a long period of time, it will eventually
cause my house to cave in.