statistics

Consider the speed of cars driving by the sidewalk. A argues that since the speed limit is 25, a good null hypothesis is that the speed is distributed as a normal random variable with a mean of 27 and a standard deviation of 3. B argues that an alternative hypothesis is that people are diving with a mean of 31 and same standard deviation.

You would like to design an empirical project that measures the speed at which cars go: it should not be that expensive to put a couple of machines in road. Now, the rental costs are non-trivial:$500 per day, measuring around 2000 car speeds per day.

a) You would like to be savvy and only collect data so the power of your test is 80%: i.e., if B is right, we will reject A null hypothesis 80% of the time. How many observations do you think A and B need to settle this problem? How much it cost?

b) How much would it cost to have a test with power of 90%?