1. 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 table gives AQI values for S02 (Sulphur Dioxide) and CO (Carbon Monoxide) from a random sample of 20 locations in California, between the years 2000 and 2010.

Location SO2 AQI CO AQI AQI Diff (SO2-CO) 1 1 3 -2 2 4 6 -2 3 3 6 -3 4 3 2 1 5 11 31 -20 6 0 8 -8 7 1 6 -5 8 27 5 22 9 7 16 -9 10 3 8 -5 11 0 7 -7 12 4 5 -1 13 7 2 UT 14 21 44 -23 15 3 5 - 2 16 3 8 -5 17 4 5 -1 18 0 2 -2 19 1 5 -4 20 9 12 -3 Summary Statistics X = 5.6; s = 7.03 X2 = 9.3; s = 10.42 X. = -3.7;s = 8.84 (a) Why are these data best regarded as a paired sample? (2 marks) (b) Do the data provide evidence that California's S02 and CO AQI levels differ, on average? Test at the 10% level of significance (8 marks) (c) Construct and interpret a 95% confidence interval for the mean difference in S02 and CO AQI levels for California. (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 against the assumption of a normally distributed population? Explain. (2 marks) Paired $02-CO AQI Values Paired $02-CO AQI Values Paired 502-CO AQI Values 10 aired Differences (802-Co requency aired Diferences (302-Go) 14 9 -20 -10 10 20 Paired Differences ($02-CO) nor quanales 3