Fuel Consumption and Cars

Suppose there are n pairs of observations and ρS is the population correlation between ranks. The four parts of a hypothesis test concerning ρS based on a normal approximation are

A turbocharger is a compact way to add more power to an automobile, by increasing the amount of air going into the cylinders. A study was conducted to examine the relationship between the added pressure (x, in psi) and power ( y, percentage change in horsepower) provided by a certain turbocharger. A variety of automobiles was selected, and a randomly selected turbocharger was installed in each. The additional air pressure and power measurements were recorded.

a. Compute Spearman's rank correlation coefficient, and use this value to describe the relationship between added air pressure and change in engine power.

b. Conduct a hypothesis test to determine whether there is any evidence that the true population correlation between ranks is greater than 0. Use a = 0.01.