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Hypothesis test: difference in proportions

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Is the water on your airline flight safe to drink? It is not feasible to analyze the water on every flight, so sampling is necessary. In August and September 2004, the Environmental Protection Agency (EPA) found bacterial contamination in water samples from the lavatories and galley water taps on 20 of 158 randomly selected U.S. flights. Alarmed by the data, the EPA ordered sanitation improvements, and then tested water samples again in November and December 2004. In the second sample, bacterial contamination was found in 29 of 169 randomly sampled flights. (a) Use a left-tailed test at alpha = .05 to check whether the percent of all flights with contaminated water was lower in the first sample. (b) Find the p-value. (c) Discuss the question of significance versus importance in this specific application. (d) Test whether normality may be assumed. (Data are from The Wall Street Journal, November 10, 2004, and January 20, 2005.)

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This solution shows detailed steps for a hypothesis test for the difference in two population proportions.

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