Explain the Difference Between a One-tailed Test and a Two-tailed Test: Quantitative Methods Assignment, NUS, Singapore

Quantitative method question.

Please explain clearly so I have a clear understanding.

(a) Explain the difference between a one-tailed test and a two-tailed test, giving an example of a case in which each would be appropriate.

(b) A road safety measure is being considered as an intervention at a site where the long-term mean frequency of injury accidents is reckoned to be 4 per year. Calculate the range of numbers of accidents occurring during a 3-year monitoring period that will indicate that this measure is effective.

(c) Show that if the true effect of the road safety measure is to reduce the mean frequency of accidents by 1/3, then the probability of it being identified as effective by monitoring a single site for 3 years is about 0.313.

(d) Calculate the corresponding probability of identifying the effectiveness of the road safety measure if 4 such sites are treated and monitored for 3 years, and comment on your results.