AP Statistics
To study the long-term effects of preschool programs
for poor children, the High/Scope Educational
Research Foundation has followed two groups of
Michigan children since early childhood. One group
of 62 attended preschool as 3 and 4 year olds. This is
a sample from population 2, poor children who
attended preschool. A control group of 61 children
from the same area and similar backgrounds
represents population 1, poor children with no
preschool. Thus the sample sizes are n1 = 61 and n2 =
62.
One response variable of interest is the need for social
services as adults. In the past 10 years, 38 of the
preschool sample and 49 of the control sample have
needed social services (mainly welfare).
Is there significant evidence that preschool reduces the
latter need for social services?
High levels of cholesterol in the blood are
associated with higher risk of heart attacks. Will
using a drug to lower blood cholesterol reduce
heart attacks? The Helsinki Heart study looked
at this question.
Middle-aged men were assigned at random to one
of two treatments: 2051 men took the drug
gemfibrozil to reduce their cholesterol levels,
and a control group of 2030 men took placebo.
During the next five years, 56 men in the
gemfibrozil group and 84 men in the placebo
group had heart attacks. Is the apparent benefit
of gemfibfozil statistically significant?
 We’re
trying to find if there is a difference.
 If there is no difference then p1 – p2 =0
 If p1 is less than p2 then p1 – p2 <0
 Two
groups from the SAME POPULATION.
 We call this a pooled sample proportion.
 Only
one value for the “population”
proportion
p = total # of successes (in both samples)
sample size 1 + sample size 2
 Use
this for the standard deviation formula
Remember
PHANTOMS
How common is behavior that puts people at
risk of AIDS? The National AIDS Behavioral
Surveys interviewed a random sample of
2673 heterosexual adults. Of these, 170 had
more than one sexual partner in the past
year. That’s 6.36% of the sample.
Estimate the true population proportion with
99% confidence.
What sample size would you need to have a
0.5% margin of error with a 99% confidence
level?
 Parameters
 Assumptions
and Conditions
 Name of the interval
 Interval (including the formulas and math to get this)
 Context
PANIC
3
4
Lyme disease is spread in the northeastern United
States by infected ticks. The ticks are infected
mainly by feeding on mice, so more mice result in
more infected ticks. The mouse population in turn
rises and falls with the abundance of acorns, their
favored food.
Experimenters studies two similar forest areas in a
year when the acorn crop failed. They added
hundreds of thousands of acorns to one area to
imitate an abundant acorn crop, while leaving the
other area untouched.
The next spring, 54 of the 72 mice trapped in the
first area were in breeding condition, versus 10 of
the 17 mice trapped in the second area. Give a
90% confidence interval for the difference between
the proportion of mice ready to breed in good
acorn years and bad acorn years.
The movie A Civil Action tells the story of a major
legal battle that took place in the small town of
Woburn, Massachusetts. A town well that supplied
water to East Woburn residents was contaminated
by industrial chemicals. During the period that
residents drank water from this well, a random
sample of 414 births showed 16 birth defects. On
the west side of Woburn, a random sample of 228
babies born during the same time period revealed
3 with birth defects.
Find a 90% confidence interval for the difference
between the two proportions.
Is it likely that the proportion of babies born with
birth defects is the same for both areas in Woburn?