Suppose an acquaintance claims to have the ability to determine the birth month of randomly selected individuals. To test such a claim, you randomly select 80 individuals and ask the acquaintance to state the birth month of the individual. If the individual has the ability to determine birth month, then the proportion of correct birth months should exceed 1/12, the rate one would expect from simply guessing.
(a) State the null and alternative hypotheses for this experiment.
(b) Suppose the individual was able to guess 9 correct birth months. The P-value for such results is 0.1726. Explain what this P-value means and write a conclusion for the test.