<NOTE: Content rearranged for 2015-2016, but not dates>
Day 1: 10.1 Comparing Two Proportions
Read p609 and articles to introduce big ideas of chapter (comparing two groups), discuss projects
Read 612–615
What is meant by “the sampling distribution of the difference between two proportions”?
It describes the possible values of and how often they will occur, where and are
the proportions of successes from two independent random samples or two treatments in a
randomized experiment.
What are the shape, center, and spread of the sampling distribution of ? Are there any conditions
that need to be met?
See box on page 614
Discuss what the SD measures—how far the estimated difference in proportions will be from the
true difference in proportions, on average.
Note that the Normal condition isn’t met for the basketball experiment.
Alternate Example: Nathan and Kyle both work for the Department of Motor Vehicles, but they live in
different states. In Nathan’s state, 80% of the registered cars are made by American manufacturers. In
Kyle’s state, only 60% of the registered cars are made by American manufacturers. Nathan selects a
random sample of 100 cars in his state and Kyle selects a random sample of 70 cars in his state. Let
be the difference in the sample proportion of cars made by American manufacturers.
(a) What is the shape of the sampling distribution of ? Why?
(b) Find the mean of the sampling distribution. Show your work.
(c) Find the standard deviation of the sampling distribution. Show your work.
(a) Because 100(0.80) = 80, 100(1 – 0.80) = 20, 70(0.60) = 42, and 70(1 – 0.60) = 28 are all ≥ 10, the sampling
distribution of is approximately Normal.
(b) The mean is
(c) Because there are at least 10(100) = 1000 cars in Nathan’s state and at least 10(70) = 700 cars in Kyle’s state,
the standard deviation is = 0.0709.
108
, Read 616–619 mention projects, start thinking about ideas
What are the conditions for calculating a two-sample z interval for ?
See box on p616
Discuss splitting 1 sample into 2 groups—OK (happens in HW)
Reminder about the grid in back of book
What is the standard error of ? How is this different than the standard deviation of ?
What does this measure?
What is the formula for a two-sample z interval for ? Is this on the formula sheet?
Alternate Example: Gun Control
Have opinions changed about gun control? Gallup regularly asks random samples of U.S. adults their
opinion on a variety of issues. In a poll of 1011 U.S. adults in January 2013, 38% responded that they
“were dissatisfied with the nation’s gun laws and policies, and want them to be stricter.” In a similar
poll of 1011 adults in January 2012, only 25% agreed with this statement.
(a) Explain why we should use a confidence interval to estimate the change in opinion rather than just
saying that the percentage increased by 13 percentage points.
Because of sampling variability, the difference of 0.13 is unlikely to be correct.
(b) Use the results of these polls to construct and interpret a 90% confidence interval for the change in
the proportion of U.S. adults who would agree with the statement about gun laws.
109
Day 1: 10.1 Comparing Two Proportions
Read p609 and articles to introduce big ideas of chapter (comparing two groups), discuss projects
Read 612–615
What is meant by “the sampling distribution of the difference between two proportions”?
It describes the possible values of and how often they will occur, where and are
the proportions of successes from two independent random samples or two treatments in a
randomized experiment.
What are the shape, center, and spread of the sampling distribution of ? Are there any conditions
that need to be met?
See box on page 614
Discuss what the SD measures—how far the estimated difference in proportions will be from the
true difference in proportions, on average.
Note that the Normal condition isn’t met for the basketball experiment.
Alternate Example: Nathan and Kyle both work for the Department of Motor Vehicles, but they live in
different states. In Nathan’s state, 80% of the registered cars are made by American manufacturers. In
Kyle’s state, only 60% of the registered cars are made by American manufacturers. Nathan selects a
random sample of 100 cars in his state and Kyle selects a random sample of 70 cars in his state. Let
be the difference in the sample proportion of cars made by American manufacturers.
(a) What is the shape of the sampling distribution of ? Why?
(b) Find the mean of the sampling distribution. Show your work.
(c) Find the standard deviation of the sampling distribution. Show your work.
(a) Because 100(0.80) = 80, 100(1 – 0.80) = 20, 70(0.60) = 42, and 70(1 – 0.60) = 28 are all ≥ 10, the sampling
distribution of is approximately Normal.
(b) The mean is
(c) Because there are at least 10(100) = 1000 cars in Nathan’s state and at least 10(70) = 700 cars in Kyle’s state,
the standard deviation is = 0.0709.
108
, Read 616–619 mention projects, start thinking about ideas
What are the conditions for calculating a two-sample z interval for ?
See box on p616
Discuss splitting 1 sample into 2 groups—OK (happens in HW)
Reminder about the grid in back of book
What is the standard error of ? How is this different than the standard deviation of ?
What does this measure?
What is the formula for a two-sample z interval for ? Is this on the formula sheet?
Alternate Example: Gun Control
Have opinions changed about gun control? Gallup regularly asks random samples of U.S. adults their
opinion on a variety of issues. In a poll of 1011 U.S. adults in January 2013, 38% responded that they
“were dissatisfied with the nation’s gun laws and policies, and want them to be stricter.” In a similar
poll of 1011 adults in January 2012, only 25% agreed with this statement.
(a) Explain why we should use a confidence interval to estimate the change in opinion rather than just
saying that the percentage increased by 13 percentage points.
Because of sampling variability, the difference of 0.13 is unlikely to be correct.
(b) Use the results of these polls to construct and interpret a 90% confidence interval for the change in
the proportion of U.S. adults who would agree with the statement about gun laws.
109
