8.4 A Significance Test for the Difference of Two Proportions
Reading Guide
In the previous section, you learned how to estimate the _______ of the difference of any two _____________________. But
sometimes you must ____________ between _____ alternatives. For example:
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Are ________________________________________________ more likely to be seriously injured?
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Have _____________________________________________ changed over the past 5 years?
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Is there a difference between the proportions of _____________________________________________________?
The __________ of the difference involved is ___________________________. All you care about is whether you have enough
__________ to conclude there is a ______________________. In this section, you will learn to perform a _______
______________________________ in order to decide if the _________________________________ can reasonably be
attributed to ___________________________ or if the _________________________________________ that something other
than _____________________________ must be causing it.
A Sampling Distribution of the Difference
You will learn about what ________________________________ you should expect in your samples when there is ____
___________________ in the proportions of success in the two ________________.
Approximate sampling distributions for samples sizes ___, ___, and ___ are shown below. In each case the proportion of successes
in the first population is ___, and the proportion of successes in the second population is ___.
Note three facts about these approximate sampling distributions:

Each sampling distribution is _____________________________ in shape and becomes more so with ___________
sample sizes.

The mean of each sampling distribution is at ______________________________________.

The formula to find the SE (_______________________) is the same as before:
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The Theory of a Significance Test for the Difference of Two Proportions
Example: Are Men More Likely to Be Left-Handed?
Perform a ___________________ to determine whether males are more likely _________________________ than ________.
1. Check conditions:
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2. Let
Let
p1 denote the proportion of __________________________________________________________________
p2 denote the proportion of __________________________________________________________________
The null hypothesis is always one of ______________________ or ______________________, so the appropriate null hypothesis
is:
The alternative hypothesis, sometimes called the ____________________, is a statement of what the researcher is
_________________________________________. Here you are looking for evidence that the proportion of _____________ is
greater ____________________. So the alternative hypothesis is:
3. Compute the test statistic and P-value. The __________________________ builds the best estimates of these _________
________________________, namely the sample proportions:
The general form of a ______________________________________is:
The difference from the sample (__________________) is ___________________________. The hypothesized difference
(______________________) is ___, the value under the null hypothesis ________________. The standard error of the estimate is
given exactly by:
You could estimate ___________ and ______________. However, you can do even better. The null hypothesis states that the
____________________________________ is equal to ___________________________________, that is __________. You can
estimate this common value of _________ by combining data from other samples into a _____________________, ___.
The pooled estimate is found by combining males and females into one group:
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The test statistic is equal to: _________, with a P-value of: __________.
The P-value is very __________, so you _________ the null hypothesis. The difference between the rates of ______________ in
these two samples is too large to attribute to _______________________. The evidence supports the alternative that
_______________________________________________________.
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