Question: A state that requires periodic emission tests of cars operates two emissions test stations, A and B, in one of its towns. Car owners have complained of lack of uniformity of procedures at the two stations, resulting in different failure rates. A sample of 400 cars at Station A showed that 53 of those failed the test; a sample of 470 cars at Station B found that 51 of those failed the test.
a. What is the point estimate of the difference between the two population proportions?
b. Construct a 95% confidence interval for the difference between the two population proportions.
c. Testing at the 5% significance level, can you conclude that the two population proportions are different? Use both the critical-value and the p-value approaches.