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Hypothesis testing for proportions

a) A state’s Division of Motor Vehicles (DMV) claims that 60% of teens pass their driving test on the first attempt. An investigative reporter examines a random sample of the DMV records for 125 teens; 86 of them passed the test on their first try. Is this good evidence that the DMV’s claim is incorrect? Carry out an hypothesis test at the .05 significance level.

b) A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacts a simple random sample of 500 current subscribers, and 137 of those surveyed expressed interest. What should the company do? Carry out a hypothesis test at the .01 significance level.

c) A roper Poll claims that 5% of U.S. adults have had vivid dreams about UFOs. You decide to test this claim and ask a random sample of 250 U.S. adults whether they have had vivid dreams about UFOs. Of those surveyed, 8% reply yes. A the .01 significance level , is there enough evidence to reject the claim?