One Proportion Z Test
p is an unknown proportion with some “success” as an
outcome.
statistic: a number that can be computed from sample
data.
p̂ (p-hat) is the sample proportion, an estimate of p, the
true proportion.
# of successful outcomes in sample
p̂ 
# of observations in sample
Conditions for Inference on a Single Proportion:
•The data are an SRS from the population of interest.
•The population is at least 10 times as large as the sample.
•For a test of H0 : p  __, the sample size n must be so
large that both np and n(1 p) are 10 or more.
•For a confidence interval, n is so large that both the count
of successes np̂ and the count of failures n(1 p̂) are 10
or more.
If these conditions are met, a 1 proportion z test (interval) is
justified.
Draw an SRS of size n from a large population with an unknown
proportion of successes, p.
An approximate level C confidence interval for p is:
p̂  z
*
p̂(1 p̂)
n
standard error (SE)
To test the hypothesis H0 : p  __, compute the z statistic
z
p̂  p
p(1 p)
n
1-Proportion Z-interval on calculator
STAT
TEST
A (1-PropZInt…)
1-Proportion Z Test on calculator
STAT
TEST
5 (1-PropZTest…)
PAGE 690 EXAMPLE 12.5
PAGE 691 EXAMPLE 12.6