AP Statistics Section 12.1 A. Now that we have looked at the principles of testing claims, we...
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Transcript of AP Statistics Section 12.1 A. Now that we have looked at the principles of testing claims, we...
AP Statistics Section 12.1 A
Now that we have looked at the principles of testing claims, we proceed to practice.
We begin by dropping the unrealistic assumption that we know the population standard deviation when testing claims
about a population mean. As with confidence intervals, this leads to the use
of ___ distributions when carrying out significance tests about .
t
One Sample t-TestDraw an SRS of size n from the population.
The one-sample t statistic:
has the t distribution with n – 1 degrees of freedom.
nsx
t 0
There is a slight change in the procedure for computing the p-value. The next examples show
this change.
.05 and .025Between
10000,19)tcdf(1.81,:5 VARS 2:84/83 ndTI
.043
17.3
.0025 and .001Between
.0025) and .001 (2 BetweenvalueP
.005) and .002 BetweenvalueP
004.)002(.2
002.)36,1000,17.3(
valuep
tcdf
These P-values are exact if the population distribution is Normal and are approximately correct for
large n in other cases.
Example: Is 98.6oF Wrong? From a random sample of 106 people, the
mean body temperature was 98.2oF with a standard deviation
of .6229. Test the common belief that the mean body temperature is
98.6oF.
Parameter: The population of interest is all people. We wish to test
Conditions:
raturebody tempemean where6.98:H vs6.98 a:0 H
.population the togeneralize
notmay results SRS,an not ifbut sample Random :SRS
Normal approx. isthat
dist. a gives CLT 106,n With :dist. x ofNormality
10nNt replacemen w/osampling are wesince andt independen
be to temp.individualexpect toReasonable :ceIndependen
Calculations:
Interpretation:
less.
actuallybut 98.6not is body temp.mean thesuggests This
98.6. is mean temp. theassume en wesmaller whor 98.2 of
mean temp. a with withsample a getting of liklihood small
verya indicates .0005, than less value,-p lowOur very
611.6
1066229.
6.982.98
t
001.)0005(.2 valuep
Test-T:2 TESTS STAT :TI83/84
If you were to choose a significance level for this test, what would it be? Why?
.H thedisprove toevidence convincing need we
so belief, heldcommonly a disprove to tryingare We01.
0
Describe a Type I and Type II error in this setting.
is.it fact in when 98.6not ismean that thegDeterminin :I Type
98.6. lower than is
it fact in when 98.6not ismean t thereject tha toFailing :II Type
Construct a 99% confidence interval for the mean body temperature and interpret it.
106
.62292.62698.2
n
stx
)36.98,04.98(
98.36 and 98.04between is population the
for raturebody tempemean that theconfident 99% are We