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The Complete Idiot's Guide to Statistics, 2nd Edition by Robert Donnelly

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Testing for Differences Between Proportions with Independent Samples

We can perform hypothesis testing to examine the difference between proportions of two populations as long as the sample size is large enough. Recall from Chapter 13, proportion data follow the binomial distribution, which can be approximated by the normal distribution under the following conditions.
np ≥ 5 and nq ≥ 5
where:
p = the probability of a success in the population
q = the probability of a failure in the population (q = 1 - p)
Let’s say that I want to test the claim that the proportion of males and females between the ages of 13 and 19 who use instant messages (IM) on the Internet every week are the same. My hypothesis would be stated as:
H0: p1

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