2. The Air Quality Index (AQ1) 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 502 (Sulphur Dioxide) and CO (Carbon Monoxide) from a random sample of 20 locations in California, between the years 2000 and 2010. Location 802 AQI CO AQI AQI Diff ($02-CO) 1 3 -2 2 4 6 -2 3 3 6 3 4 3 2 1 15 |11 31 -20 TO 8 7 1 6 8 5 19 10 11 12 13 14 15 5 16 3 8 17 4 5 18 0 19 1 5 20 9 12 -3 Summary Statistics X = 5.6; 5 = 7.03 I, = 9.3:5 = 10.42 I =-17:5 = 8.84 (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 AQ1 levels differ, on average? Test at the 10% level of significance (B marks) 2 STAT 151 Assignment 5 Total: 97 marks [c) Construct and interpret a 95% confidence interval for the mean difference in 502 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 501-CO AOl Valens 3. According to an online source, 79.8% of students are right-handed in Alberta secondary schools, 7.9% are left-handed, and 12.3% are ambidextrous (source: Census at School Canada, 2018-2019). A researcher wishes to test if these percentages seem reasonable among the general population of Albertans, so she obtains a random sample of 200 Albertans, from which she obtains the following frequency distribution: Handedness Right-Handed Left-Handed Ambidextrous Frequency 137 45 18 Does the above give evidence to suggest the proportions of right-handed, left-handed, and/or ambidextrous Albertans differ from the proportions stated in the online source? Test at the 1% significance level. (8 marks]