Question

Is the water on your airline flight safe to drink? It isn’t 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 gallery water taps on 20 of 158 randomly selected U.S. flights. Alarmed by the data, the EPA ordered sanitation improvements and then tested the water samples again in November and December of that year. In the second sample, bacterial contamination was found in 29 of 169 randomly sampled flights. a. Calculate the proportion of the water sample that was contaminated in each period surveys. b. Construct a 95 percent confidence interval for each period’s survey. c. Can you rule out the possibility that there was no change in water contamination? Carefully explain.

Answer 1

Solution: Hypothesis : T = Percent of flights will contaminated watey in first sur 2= Percent of flights with contaminated water in second sample - Nul Hypothese = Ho 12 Altep native hypothesis : Htiye Decision Rule: For alett -tailed test, we want the left-tail area to be do.s. --1-645 The critical value of a that accomplishes this is 2005 so the decision rule is . Reject Ho if z z-1-645 otherwise do not reject to samme proportions' Given X2 =20, 11-158, X2 = 29, ng=169 and oc=015 Pin e muito tempo = -1866 Pa = x2 = ña e = 1.716 Test statistic 2= P.-P2 ✓ PCI-P) (t + where prxt12 I nit02 Petting value of Ps Botting out 1498 1587169 2- .266 -1716 149861--1498) Csat ton = -1-1396 Decibioni- since the test statistic (2=-1,1396) is greater than Critical Yale (-1,645) Serbined with we failto reject to SOM

There is no statistical evidence to conclude that the percent of flights with contaminated wath was lowed in the first sample for finding the left -tailed area for 2=-1•1396 by using the function - 1 - NORMDIST (-1 1390) in Excel! P-value =P(Z >L-1.1396) = -1272 The dif blu Proportation is not sign of individual passengers is concerned, The alt is important. Normality can be assumed because no palo for both samples. Cs Scanned with CamScanner