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## AP Statistics Section 13.2 B

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**An observed difference between two sample proportions can**reflect a difference in the populations or it may just be due to chance variation in random sampling. Significance tests help us decide if the effect we see in the samples is really there in the populations. The null hypothesis says that _________________ between the two populations: . The alternative hypothesis says what kind of difference we expect.**In a significance test, we always assume___________________.**So, if we assume there is no difference in the populations, then all the observations in both samples really come from _______________. So instead of estimating separately, we combine the two samples and use the overall sample proportion to estimate the single population parameter p.**Using in place of both in the**expression for the standard error SE of gives**Example 13.12: The movie A Civil Action tells the following**story. A town well that supplied water to East Woburn, Massachusetts residents was contaminated by industrial chemicals. During the period that residents drank water from this well, a sample of 414 births showed 16 birth defects. On the west side of Woburn, a sample of 228 babies born during the same time period revealed 3 birth defects. The plaintiffs suing the companies responsible for the contamination claimed that these data show that the rate of birth defects was significantly higher in East Woburn, where the contaminated well water was in use. How strong is the evidence supporting this claim? What should the judge for this case conclude?

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