Confidence Interval Example, Proportion
A sample of 500 nursing applications included 60 from men. Find the 90%
confidence interval of the true proportion of men who applied to the nursing
program.
Using Formulas
Want the 90% confidence interval so α = 0.10. Since we may be wrong both
high or low we need to divide α by 2.
n = 500
x = 60
60
= 0.12
500
qˆ = 1 − pˆ = 0.88
pˆ =
0.05
0.05
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€
Zα = −1.645
Zα = 1.645
2
€
Error term here is E = Zα
interval is
2
2
pˆ qˆ €
= 1.645
n
0.12 – 0.024 < P€< 0.12 + 0.024
⇒
(0.12)(0.88)
500
= 0.0239063272 , so the
0.096 < P < 0.144
Now using the calculator:
Press: STAT
X: 60
n: 500
C-Level:0.90
Calculate
←
1-PropZInt
⇒
1-PropZInt
(.0961, .1439)
pˆ = .12
n = 500
So the 90% confidence interval is: (0.0961,
0.1439).
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