4. (16 marks) The Air Quality Index (AQI) is used to measure air quality near roadways and industrial regions in large cities. Governments report AQI values for common pollutants to keep the public informed about air quality. AQI values of 0-50 are regarded as good, 51-100 as moderate, 101-150 as unhealthy for sensitive individuals, 151-200 as unhealthy, 201-300 as very unhealthy, and beyond 300 as hazardous. The following data are a random sample of 20 AQI values for NO2 (Nitrogen Dioxide), in Scottsdale Arizona, between the years 2000 and 2010. The sample mean is x = =37.95 and the sample standard deviation is s = 18.58. 97 8 39 32 37 56 42 54 21 38 31 38 50 34 28 27 20 52 34 21 (a) Test if the average NO2 AQI is good (less than 50) in Scottsdale Arizona. Complete all 6 steps of your hypothesis test, including a discussion of the assumptions. Use the 1% significance level (8 marks) (b) Obtain and interpret a 99% two-sided confidence interval mean NO2 AQI level in Scottsdale Arizona. (6 marks) (c) An independent study estimates that the average NO2 AQI level is 35 in Arizona. Does the interval in part (b) provide evidence to suggest the true mean is equal to 35? Why or why not? (2 marks)