One Prop Z-Test
Steps
One Proportion Z Interval
P
p = proportion of _________ who
_____________
C
Random: SRS
Normality: n p  10 and n(1  p)  10
Independence: pop ≥ 10n
F
One Prop Z Interval (_____, ______)
S
We are ______% confident that the
interval captures the true proportion of
__________ who _________.
Steps
One Proportion Z Test
P
p = proportion of _________ who
_____________
H0: p = ______
Ha: p
______
C
Random: SRS
Normality: np0  10 and n(1  p0 )  10
Independence: pop ≥ 10n
F
One Prop Z Test
Z = ________
p = ________
S
Since p
α, we reject/fail to reject H0.
We conclude/cannot conclude that
__________________________.
• I say “Normal” you say _________________.
• So, the calculator is calculating a Z score based on the sampling
distribution of p
statistic  parameter
z
standard deviation of the statistic
• Then, it uses Table A to calculate the probability.
• We are lucky. We have calculators. Yay, TI.
• A potato-chip producer has just received a truckload of
potatoes from its main supplier. If the producer determines that
more than 8% of the potatoes in the shipment have blemishes,
the truck will be sent away to get another load from the
supplier. A supervisor selects a random sample of 500 potatoes
from the truck. An inspection reveals that 47 of the potatoes
have blemishes. Carry out a significance test at the α= 0.10
significance level. What should the producer conclude?
• Remind me, what is a p-value???
• In the context of the last problem, describe the
following:
• Type I Error
• Type II Error
• Power
• I claim that I am an 80% free throw shooter. You think I am
overestimating my ability and challenge me to a 50 shot trial.
In my trial, I make only 32 shots. Is the difference statistically
significant at the α = 0.05 level? What if α = 0.01?
• At the conclusion of a significance test, we have made a
decision.
• We either reject H0 or we fail to reject H0.
• But, we’re left wondering, what is a good estimate of the true
value of p (the population proportion)?
• A confidence interval can shed light on this!
According to the Centers for Disease Control and
Prevention (CDC) Web site, 50% of high school
students have never smoked a cigarette. Jason
wonders whether this national result holds true in
his large, urban high school. For his AP Statistics
class project, Jason surveys an SRS of 150
students from his school. He gets responses from
all 150 students, and 90 say that they have never
smoked a cigarette. What should Jason conclude?
Give appropriate statistical evidence to support
your answer.
• For his AP Statistics class project, Jason surveys an SRS of 150
students from his school. He gets responses from all 150
students, and 90 say that they have never smoked a cigarette.
Construct a 95% confidence interval for p, the proportion of
students at Jason’s school who say they have never smoked a
cigarette.
• Don’t forget to recheck the normality condition!
• Confidence Intervals and Two-Sided Tests
There is a link between confidence intervals and two-sided tests. The 95% confidence
interval gives an approximate range of p0’s that would not be rejected by a two-sided
test at the α = 0.05 significance level. The link isn’t perfect because the standard error
used for the confidence interval is based on the sample proportion, while the denominator
of the test statistic is based on the value p0 from the null hypothesis.
 A two-sided test at significance level α
(say, α = 0.05) and a 100(1 –α)%
confidence interval (a 95% confidence
interval if α = 0.05) give similar
information about the population
parameter.

the sample
proportion
falls in the
 IfHowever,
if the
sample proportion
“fail
H0” region,
like the
falls to
in reject
the “reject
H0” region,
thegreen
value
in the
figure,
the resulting
95%
resulting
95%
confidence
interval
would
confidence
would
p0. In
not include interval
p0. In that
case,include
both the
that
case, both
significance
test and
significance
testthe
and
the confidence
the
confidence
be unable
interval
would interval
provide would
evidence
that p0
to
rulethe
outparameter
p0 as a plausible
is not
value. parameter
value.
• A two-sided test of H0 : p = p0 at significance level α gives
roughly the same conclusion as a 100(1 – α)% confidence
interval.
• CAUTION: This duality does not apply to onesided significance tests and confidence
intervals!
• From the output above, see if you can identify
•
•
•
•
H0 and Ha
All the necessary components of the “formula” step
The conclusion (reject or fail to reject)
The duality between the CI and the hypothesis test