3. The Air Quality lndex [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 AQl 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 l5] Assignment 5 Total: I l0 Marks A'l Difl' SDICO lillllllli E l a NI ____ Mf=5u6s=103 x=9.-3s=1o.42 =-3.-7s=a.34 [a] Why are these data best regarded as a paired sample? [2 marks] [b] Do the data provide evidence that California's $02 and CO AQ] levels differ, on average? Test at the 5% level ofsignimnce [8 marks) [c] Construct and interpret a 90% condence interval forlhe mean difference in $02 and CO AQl 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 marks] [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]