Is the water on your airline fight safe to drink? It is not feasible to analyze the water on every fight, so sampling is necessary. 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. fights. Alarmed by the data, the EPA ordered sanitation improvements, and then tested water samples again. In the second sample, bacterial contamination was found in 29 of 169 randomly sampled fights.
(a) Use a left-tailed test at α = .05 to check whether the percent of all fights 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 of p1 – p2 may be assumed.