In polluted areas of Texas, registered vehicles must undergo an annual emissions inspection. In Fort Bend County (near Houston), 27 vehicles failed the emissions test, from among 200 randomly selected vehicles.
(a) Does this data provide compelling evidence for concluding that more than 10% of all Fort Bend County vehicles will fail the emissions test? State and test the appropriate hypotheses using a significance level of .05. In reaching your conclusion, what type of error might you have committed?
(b) Repeat the test in part (a) using a significance level of 0.25. In reaching your conclusion, what type of error might you have committed?
(c) If it is really the case that 15% of all Fort Bend County vehicles fail the emissions test, how many vehicles would have to be tested to have probability of type II error equal to 10% for the test in part (b)?