Confidence Intervals
Teens, Smartphones & Texting
Texting Volume Is Up while the Frequency of
Voice Calling Is Down
Smartphones are gaining teenage users. Some 23% of all
those ages 12-17 say they have a smartphone and
ownership is highest among older teens: 31% of those ages
14-17 have a smartphone, compared with just 8% of youth
ages 12-13.
Recall Sampling Distributions
The statistics quoted by PEW Research are based on a
sample. Let’s say that exactly 30% of all teens age 14 to
17 in the U.S. have a smartphone.
If we were to take a random sample of 40 teens age 14
to 17 and record the proportion that had a
smartphone, what proportions would be reasonably
likely in our sample? In other words, if we did many
such samples, the middle 95% of sample proportions
would be between _____ and ______.
Recall Sampling Distributions
A normal model is appropriate, because . . .
So the middle 95% of sample proportions should fall
within 1.96 standard deviations of 0.30.
or 0.158 and 0.442.
Suppose that in a random sample of 40 retired women, 45% of the
women travel more than they did while they were working. Find
the 95% confidence interval for the proportion of all retired
women who travel more.
Capture Rate
Here is a set of 100 confidence intervals created from
100 random samples of size 40. p = 0.45.
Source: 2010 AP Exam
Unfortunately, we wouldn’t know the standard deviation is 107.
We’d have to estimate the standard deviation using the sample
standard deviation.
We adjust for this by changing the critical value. We don’t use
the cutoffs for the normal distribution (z), we use an adjusted
value called t.
t is larger than z, so it make the intervals wider, and therefore
more likely to capture the population mean. In this case we
use t = 3.182 for 3 degrees of freedom. (df = n – 1)
Source: 2002 AP Exam
Answer: A
Source: 2002 AP Exam
Answer: E
Source: 2002 AP Exam
Answer: D
1. USA Today reported that speed skater Bonnie Blake had “won the USA’s heart,”
according to a USA Today/CNN/Gallup poll conducted on the final Thursday of the 1994
Winter Olympics. When asked who was the hero of the Olympics, 65 percent of the
respondents chose Blair, who won five gold medals. The poll of 615 adults, done by
telephone, had a margin of error of 4 percent. Which of the following statements best
describes what is meant by the 4 percent margin of error?
(A) About 4 percent of adults were expected to change their minds between the time of
the poll and its publication in USA Today.
(B) About 4 percent of adults did not have telephones.
(C) About 4 percent of the 615 adults polled refused to answer.
(D) Not all of the 615 adults knew anything about the Olympics.
(E) The difference between the sample percentage and the population percentage is
likely to be less than 4 percent.
Source: 1997 AP Exam
Answer: E
Source: 2009 AP Exam
Sample Paper A
Sample Paper A
Sample Paper A
Sample Paper A
Sample Paper B
Sample Paper B
Sample Paper B
Sample Paper C
Sample Paper C
Sample Paper C

similar documents