AP Statistics
Confidence Interval
In-Class Example
A May 2002 Gallup Poll found that only 8% of a random sample of 1012 adults approved of
attempts to clone a human being. Use this result to predict with 95% confidence the
proportion of all adults that approves of attempts at human cloning.
BIG IDEA: I don’t (can’t) know the actual proportion of all people in the population who
approve of attempts at cloning, but I will be satisfied if I can use my sample to
generate an estimate – in the form of an interval – that I can say, with 95% confidence,
will capture the actual proportion.
a. What is meant by the phrase “predict with 95% confidence”?
It means that there is only a 5% chance that the actual proportion of people
who approve of attempts at cloning will be outside the range of values I
come up with.
b. What is the critical value z* that goes with a 95% confidence level?
The z* value that corresponds to a 95% confidence level is z* = 1.96.
c. Find the margin of error for this poll if we want 95% confidence in our estimate.
The margin of error (ME) = z *
pˆ(1  pˆ)
(.08 )(.92 )
= 1 .96
= .0167
n
1012
d. Explain what the margin of error means in this context.
The ME is how far my interval extends above and below my sample statistic.
In this case my interval extends .0167 on either side of .08.
e. Find the 95% confidence interval.
The resulting confidence interval is between .0633 and .0967.
f. State your conclusion.
I am 95% sure that between 6.33% and 9.67%. of all people (in the
population from which this sample was taken) approve of attempts at cloning
humans.