The correct answer is option a, a z-test of a population proportion.
The z-test is an appropriate statistical method to examine a hypothesis relating to a population proportion, especially in cases where you're conducting a one-tailed test. The z-test takes into account known population parameters, like population proportion and standard deviation.
Option b and c, which refer to the chi-square goodness-of-fit test and the chi-square test of independence, respectively, are not apt for a one-tailed test of a population proportion. The chi-square goodness-of-fit test is designed to find out if an observed frequency distribution fits a particular theoretical model, and the chi-square test of independence is used to determine the relationship between two categorical variables.
Options d and e are incorrect because they either negate all the testing methods or erroneously agree with all.
Thus, to apply a one-tail test of a population proportion, the z-test of a population proportion would be the appropriate statistical test to use.