Question

Club used to have pigeon races from Ohio to Coney Island.

The times of 5 randomly selected birds were

7 hours, 53 minutes
8 hours, 10 minutes
8 hours, 23 minutes,
8 hours, 42 minutes
8 hours, 52 minutes.

Assuming the pigeon finishing times are normally distributed test the hypothesis that the average pigeon can make the 400 mile run in 8.5 hours vs the alternative that the true average speed is faster than that.

Why do you need the assumption that the pigeon finishing times are normally distributed for your method to work? Is there any reason that assumption should be true?

Answer 1