Via Rail recently installed new passing tracks and a Centralized Traffic Control system on the line between Kingston and Ottawa in order to reduce delays. Suppose that, before the improvements, trains between Kingston and Ottawa were on average 12.4 minutes late. After the improvements, a consumer group monitored delays during a period of three months. For a random sample of 35 trains, it found the average delay to be 6.2 minutes with a standard deviation of 8 minutes. “The improvements reduced delays by half,” they claimed.

a) Have average delays been reduced? State your hypotheses and calculate a P-value. State any assumptions you’re making and whether they’re likely to be true.

b) Calculate the 95% confidence interval for the delays after the improvements, assuming the conditions are satisfied. Comment on the validity of your confidence interval.

c) Comment on the ethics of the consumer group’s statement.