Refer to Exercises 3 and 4. An atmospheric scientist notices that the slope of the least-squares line in the study described in Exercise 4 differs from the one in the study described in Exercise 3. He wishes to test the hypothesis that the effect of humidity on ozone level differs between the two cities. Let βA denote the change in ozone level associated with an increase of 1 percent relative humidity for the city in Exercise 3, and βB denote the corresponding increase for the city in Exercise 4.
a. Express the null hypothesis to be tested in terms of βA and βB.
b. Let βA and βB denote the slopes of the least-squares lines. Assume these slopes are independent. There are 120 observations in each data set. Test the null hypothesis in part (a). Can you conclude that the effect of humidity differs between the two cities?