Water hardness. In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, or ppm) in the drinking water. Here are the scatterplot and regression analysis of the relationship between mortality and calcium concentration, where the dependent variable is Mortality.

a) Is there an association between the hardness of the water and the mortality rate? Write the appropriate hypothesis.

b) Assuming the assumptions for regression inference are met, what do you conclude?

c) Create a 95% confidence interval for the slope of the true line relating calcium concentration and mortality.

d) Interpret your interval in context.

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Variable Coeff SE(Coeff) Intercept 1676.36 29.30 Calcium -3.226 0.485 R squared 42.9% s=143.0 with 61-2-59 degrees of freedom 2000- 1800- 1600- 1400- Mortality (deaths/100,000) 1200- 30 60 90 120 Calcium (ppm)