AP Statistics
Sections 8.1 & 8.2 Practice
Name: _____________________________________
1. A recent poll found that “433 of the 1548 randomly-selected adults questioned felt that unemployment compensation should be
extended an additional six months while the country is in its current economic downturn.” We want to use this information to
construct a 95% confidence interval to estimate the proportion of the U.S. adults who feel this way.
a) State the parameter our confidence interval will estimate.
b) Identify each of the conditions that must be met to use this procedure, and explain how you know that each one has been satisfied.
c) Find the appropriate critical value and the standard error of the sample proportion.
d) Give the 95% confidence interval.
e) Interpret the confidence interval constructed in part (d) in the context of the problem.
f) Suppose you wanted to estimate the proportion of people who feel that unemployment compensation should be expanded with 95%
confidence to within ± 1.5%. Calculate how large a sample you would need.
g) If you wanted to have a margin of error of ±1.5% with 99% confidence, would your sample have to be larger, smaller, or the same
size as the sample in part (f)?
2. A consumer watchdog organization estimates the mean weight of 1-ounce “Fun-Size” candy bars to see if customers are getting full
value for their money. A random sample of 25 bars is selected and weighed, and the organization reports that a 90% confidence
interval for the true mean weight of the candy bars is 0.992 to 0.998 ounces.
a) What is the point estimate from this sample?
b) What is the margin of error?
c) Interpret the 90% confidence interval 0.992 to 0.998 in the context of the problem.
d) Interpret the confidence level of 90% in the context of the problem.
3. A national health organization warns that 30% of the middle school students nationwide have been drunk. Concerned, a local health
agency randomly and anonymously surveys 110 of the 1212 middle school students in its city. Only 21 of them report having been
drunk.
a) What proportion of the sample reported having been drunk?
b) To keep the margin of error at most 5% with 80% confidence, how many middle school students do we need to survey?
4. Find the sample size needed to estimate the proportion of voters favoring a candidate if we want our estimate to be within 3% with
95% confidence.
5. A pollster is hired to determine the percentage of voters favoring the Republican presidential nominee. If we require 99%
confidence that the estimated value is within 2% of the true value, how large should the sample be?
6. Multiple Choice: The New York Times and CBS News conducted a nationwide poll of 1048 randomly selected 13- to 17-year-olds.
We can consider the sample to be a SRS. Of the 1048 teens surveyed, 189 named Fox as their favorite television network. A 90%
confidence interval for the proportion of all people in this age group who would choose Fox as their favorite network is (0.1608,
0.1998). Suppose you were to change the confidence level to 95% using the same sample. How would the confidence interval
change? No calculations necessary.
a) The confidence interval would be the same width but shifted to the left.
b) The confidence interval would be the same width but shifted to the right.
c) The confidence interval would have the same center but be wider.
d) The confidence interval would have the same center but be narrower.
7. True or False: Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of
confidence, and the margin of error. Determine whether the statement is true or false.
a) For a given sample size, higher confidence means a smaller margin of error.
b) For a specified confidence level, larger samples provide smaller margins of error.
c) For a fixed margin of error, larger samples provide a greater confidence.
d) For a given confidence level, halving the margin of error requires a sample twice as large.
e) For a given sample size reducing the margin of error will mean lower confidence.
f) For a certain confidence level, you can get a smaller margin of error by selecting a bigger sample.
g) For a fixed margin of error, smaller samples will mean lower confidence.
h) For a given confidence level, a sample 9 times as large will make a margin of error one third as big
8. Suppose a 90% confidence interval is stated as (0.3011, 0.4189).
a) What is the sample proportion from this sample?
b) What is the margin of error?
9. A newspaper article indicates that an estimate of the unemployment rate involves a sample of 47,000 people. If the reported rate
must be within 0.2% and the rate is known to be 8%, find the corresponding level of confidence.
10. A medical research team feels confident that a serum they have developed will cure about 75% of the patients suffering from a
certain disease. How large should the sample size be for the team to be 98% confident that the sample proportion of the cures is within
4% of the proportion p of population cures?
11. A sociologist wishes to estimate the proportion of Catholic residents in one region who hold favorable attitudes toward the concept
of ordaining women as priests. She wishes the interval estimate to be within 3% with 99% confidence. A reasonable planning value
for p from past studies is 0.40. What is the required sample size to achieve the desired accuracy?