Download AP Statistics Review

AP Statistics Review
Chapter 18 and 19
Name: __________________________
Review the problems from the text from Chapters 18 and 19.
Review the problems from the Chapter 18 Worksheet and the Chapter 19
Worksheet.
 Pay attention to those problems where you need to use expected value and
standard deviations from those expected values. (see pg. 430, 29, 41 and see
chapter 18 worksheet #8)
 Pay attention to those problems where you need to find sample size. (see pg.
449, #29, 31, 33 and see Chapter 19 worksheet, #3, 4, and 5)
 Make sure you pay attention to problems that differentiate between using a
sampling distribution and a distribution of the population. (see pg. 430, #25
and 26 and see Chapter 18 Worksheet, #7)
 Know your conditions.
 Make sure you can explain the logic behind the topics in these chapters.
(The above is NOT a complete list of the topics on the quiz—it is meant to
highlight concepts that many students find difficult or forget to study for the
quiz. You really should know how to do ALL the problems in the text and on
the worksheets, as well as understanding the notes from class)
Sample Problems:
1. It is believed that 4% of children have a gene that may be linked to juvenile
diabetes. Researchers hoping to track 20 of these children for several years
test 732 newborns for the presence of this gene. What is the probability that
they find enough subjects for their study? Check your conditions.
2. Herpetologists (snake specialists) found that a certain species of reticulated
python have an average length of 20.5 feet with a standard deviation of 2.3
feet.
a. What is the probability that a snake of this species of python is found
that has a length that is over 25 feet long?
b. A group of scientists have collected a random sample of 30 adult
pythons and measured their lengths. In their sample, the mean length
was 19.5 feet. One of the herpetologists fears that pollution might be
affecting the natural growth of pythons. Do you think that this sample
result is unusually small? Explain. Make sure to check conditions.
3.
A statistics professor asked her students whether of not they were registered
to vote. In a sample of 50 of her students (randomly sampled from her 700
students), 35 said they were registered to vote.
a. Find a 95% confidence interval for the true proportion of the
professor’s students who were registered to vote. Make sure to check
any necessary conditions and to state a conclusion in the context of the
problem.
b. Explain what 95% confidence means in this context. (this is different
than interpreting that interval)
c. What is the probability that the true proportion of the professor’s
students who were registered to vote is in your confidence interval?
(this is a difficult question—think about what a confidence interval
tells us and does not tell us. What does it say about the sample that
was collected?)
d. According to a September 2004 Gallup poll, about 73% of 18 to 29
year-olds said that they were registered to vote. Does the 73% figure
from Gallup seem reasonable for the professor’s students? Explain.
e. If the professor only knew the information from the September 2004
Gallup poll and wanted to estimate the percentage of her students who
were registered to vote to within  4% with 95% confidence, how
many students should she sample?
4. How would you best be able to decrease the margin of error of your 95%
confidence interval, but leave the confidence level at 95%?
5. How would you best be able to decrease your margin of error, while also
increasing your confidence level? What would be the advantage of this? The
disadvantage of this?
6. The scores on a national exam given to all 8th graders is skewed left with a
mean of 84% and a standard deviation of 3%.
a. Suppose we took repeated samples of 5 students and calculated the
mean of those 5 students in each sample. The sampling distribution of
these mean scores would most likely have what shape?
b. If we wanted our sampling distribution of these mean scores to be
symmetric, what would have to occur?
7. Suppose we randomly sampled a large number of middle school males and
determined that the 95% confidence interval for their mean weights is
(100,150).
a. What was the sample mean for this sampling distribution of mean
weights of male middle school students?
b. What is the standard error for the sampling distribution of mean
weights of male middle school males?
c. What is the margin of error for the sampling distribution of mean
weights of male middle school students?
d. Interpret the 95% confidence interval.
e. Suppose a study was conducted 15 years ago that found that the
average middle school male student weighed 110 pounds. Should
people conclude that the mean weight of middle school students today
is higher than what is was 15 years ago? Explain.