Quiz 10.1A
AP Statistics
Name:
Suppose you administer a certain aptitude test to a simple random sample of 9 students in your school,
and that the average score is 105. From past experience, scores on such a test among students like
those at your school follow a Normal distribution. We want to determine the mean score µ of the
population. Assume a standard deviation of
= 15 for the test.
1. What is the upper critical value for a 98% confidence interval? (Show the key numbers in the
sketch of the distribution.)
2. Construct and interpret a 98% confidence interval for
the mean score µ. Follow the Inference Toolbox.
3. Explain the meaning of “98% confident.”
4. What sample size would be needed to have a margin of error of at most 4 points (still with 98%
confidence)? Show your work.
Chapter 10
Quiz 10.1B
Quiz 10.1B
AP Statistics
Name:
Suppose your class is investigating the weights of Snickers 1-ounce Fun-Size candy bars to see if
customers are getting full value for their money. Assume that the weights are Normally distributed
with standard deviation
= 0.005 ounces. Several candy bars are randomly selected and weighed
with sensitive balances borrowed from the physics lab. The weights are
0.95 1.02 0.98 0.97 1.05 1.01 0.98 1.00
ounces. We want to determine a 90% confidence interval for the true mean, µ.
1. Determine z*. (Show your work, including a sketch of the distribution.)
2. Calculate and interpret a 90% confidence interval for the mean
weight of the candy bars. Follow the Inference Toolbox.
3. Explain the meaning of the confidence level.
4. Determine the sample size you would need to estimate µ within 0.001 at a 90% confidence level.
Chapter 10
Quiz 10.1B
Quiz 10.2A
AP Statistics
Name:
National Fuelsaver Corporation manufactures the Platinum Gasaver, a device they claim “may increase
gas mileage by 22%.” Here are the percent changes in gas mileage for 15 identical vehicles, as
presented in one of the company’s advertisements:
48.3 46.9 46.8 44.6 40.2 38.5 34.6 33.7 28.7 28.7 24.8 10.8 10.4 6.9 12.4
1. Construct and interpret a 90% confidence interval to estimate the mean fuel savings in the
population of all such vehicles. Follow the Inference Toolbox.
2. Explain what “90% confidence” means in this setting.
3. Comment on the manufacturer’s claim based on your work in Question 1.
Chapter 10
Quiz 10.1B
Quiz 10.2B
AP Statistics
Name:
About 42,000 high school students took the AP Statistics exam in 2001. The free-response section of
the exam consisted of five open-ended problems and an investigative task. Each free-response question
is scored on a 0 to 4 scale (with 4 being the best). A random sample of 25 student papers yielded the
following scores on one of the free-response questions:
1 0 1 0 0 0 3 1 1 1 0 2 0 0 2 1 1 0 2 4 1 0 2 0 3
1. Is a sample of 25 papers large enough to provide a good estimate of the mean score of all 42,000
students on this exam problem? Justify your answer.
2. Do you think the population of scores on this question is Normally distributed? Explain why or
why not.
3. Construct and interpret a 95% confidence interval for the mean score on this exam question.
Follow the Inference Toolbox. Be sure to explain why it’s okay to calculate the interval in light of
your answer to Question 2.
Chapter 10
Quiz 10.1B
Quiz 10.3A
AP Statistics
Name:
A New York Times poll on women’s issues interviewed 1025 women randomly selected from the
United States, excluding Alaska and Hawaii. The poll found that 47% of the women said they do not
get enough time for themselves.
1. The poll announced a margin of error of ±3 percentage points for 95% confidence in its
conclusions. Do you agree with this margin of error? If so, explain why. If not, tell why not.
2. What is the 95% confidence interval from this poll result? Interpret the interval in context.
3. What conditions must be met in order for the confidence interval in Question 2 to be valid? Check
whether each of those conditions is satisfied in this case.
4. Explain to someone who knows no statistics why we can’t just say that 47% of all adult women do
not get enough time for themselves.
5. Explain clearly what “95% confidence” means.
Chapter 10
Quiz 10.1B
Quiz 10.3B
AP Statistics
Name:
A news article on a Gallup Poll noted that “28 percent of the 1548 adults questioned felt that those who
were able to work should be taken off welfare.” The article also said, “The margin of error for a
sample size of 1548 is plus or minus three percentage points.”
1. Opinion polls usually announce margins of error for 95% confidence. Using this fact, explain to
someone who knows no statistics what “margin of error plus or minus three percentage points”
means.
2. Do you agree with the margin of error stated in the poll results? If so, explain why. If not, tell why
not.
3. What is the 99% confidence interval from this poll? Interpret the interval in context.
4. What conditions must be met in order for the confidence interval in Question 3 to be valid? Check
whether each of those conditions is satisfied in this case.
5. This poll was conducted by telephone. Explain how undercoverage could lead to a biased estimate
in this case.
Chapter 10
Quiz 10.1B