5. (26 marks) In studying the effect of air quality on a lake, the experimenter takes observations on the pH of the water and the air quality as measured on an air quality index. The index goes from 0 and 100 with larger numbers representing high pollution. Theses data are obtained: PH (a) 4.5 4.1 4.8 4.0 5.0 6.0 3.5 4.9 3.2 6.1 Air quality (y) 40 50 60 20 10 70 30 85 15 (a) Estimate the correlation coefficient. (2 marks) (b) Test at the 0.05 significance level for a significant non-zero correlation. (6 marks) (c) Estimate the linear regression equation to predict the air quality by pH of the water. (4 marks) (d) Test at the 0.05 significance level that the slope of the linear regression equation is not zero. (6 marks) (e) Predict the air quality when the pH of the water is 5.5. Do you find any problem on the predicted value? (4 marks) (f) Predict the air quality when the pH of the water is 7.0. Do you find any problem on the predicted value? (4 marks)