3. The Air Quality Index [AQI] is used to measure air quality near roadways and industrial regions in large cities. Governments report AQ] 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 table gives AQI values for $02 (Sulphur Dioxide] and CO [Carbon Monoxide] from a random sample of 20 locations in California. between the years 2000 and 2010. STAT IS] Assignment 5 Tolol: 1 l0 Marks An] leI' EOECO _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ \\J *4 N ____ ____ ____ \"m i = 9.3-s = 10.42 i. = -3.7-s = 8.84 [a] Why are these data best regarded as a paired sample? [2 marks) 0:] Do the data provide evidence that California's S02 and CO AQ] levels differ. on average? Test at the 5% level ofsig'nicance [0 marks) [c] Construct and interpret a 90% condence interval for the mean difference in 502 and CO AQ] levels forCalifornia. [6 marks] [d] Does the interval from [c] lead to a conclusion that agrees with the test from [b]? Explain why or why not. (2 marls] [e] The following plots display the sample distribution of paired differences. Do the plots provide any clear indication agath the assumption of a normally distributed population? Explain. (2 marks]