A random sample of 46 college students were asked if they were doing community service work during a particular semester. The following table gives the data, comparing men and women. Do the data provide sufficient evidence to conclude that men are less likely than women to be involved in community service?

(a) Consider a chi-square test against a directional alternative with α = 0.05. The value of the test statistic is 3.45. Give bounds for the P-value and state the conclusion that you reach in the context of the problem.
(b) Now consider Fisher's Exact Test, with a directional alternative, which involves calculating the probabilities of several possible 2 × 2 tables. Don't calculate any probabilities. Instead, state the number of tables for which the probability would need to be calculated if you were to carry out the test.

Community service Yes Male Female Total No 18 12 30 Total 23 23 46 16