Question

During the zombie apocalypse, one of the primary objectives is to not get bit by a zombie. The current proportion of the population getting bit by zombies is 0.6 (which doesn’t look good for the future of humankind). Special forces zombie evader, Rick Grimes, believes his very risky tactics will actually reduce the proportion of bite incidences. Suppose Rick takes a random sample of 30 individuals (with their consent) to put his tactics to the test. The group goes out into the unprotected zone, and upon return it is noted that 15 members of his group had gotten bit by a zombie.

(a) Use the sample data to compute the 95% Confidence Interval for the population proportion of individuals who get bit by zombies under Rick’s tactics. Interpret your interval in context of the problem.

(b) Perform a 4-step hypothesis test to assess the effectiveness of Rick’s tactics. In particular, is the population proportion of individuals getting bit by zombies under Rick’s tactics less than the current rate of 60%? Provide the null and alternative hypothesis in math notation.

(c) Write out the Type 1 and Type 2 errors in context of the problem. Discuss which error you feel is the worse error to commit in this scenario.

Answer 1

The solution to this problem is given by