R5.30. Hard water 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 anal- ysis of the relationship between mortality and calcium concentration. Dependent variable is Mortality R-squared = 43% s = 143.0 with 61 - 2 = 59 degrees of freedom Variable Intercept Calcium Mortality (deaths/100,000) 2000 1800 1600 1400 1200 Coefficient 1676 -3.23 30 SE(Coeff) 29.30 0.48 60 90 Calcium (ppm) 120 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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R5.30. Hard water 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 anal-
ysis of the relationship between mortality and calcium
concentration.
Dependent variable is Mortality
R-squared = 43%
s = 143.0 with 61 - 2 = 59 degrees of freedom
Variable
Intercept
Calcium
Mortality (deaths/100,000)
2000
1800
1600
1400
1200+
Coefficient
1676
-3.23
30
SE(Coeff)
29.30
0.48
90
60
Calcium (ppm)
120
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.
Transcribed Image Text:R5.30. Hard water 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 anal- ysis of the relationship between mortality and calcium concentration. Dependent variable is Mortality R-squared = 43% s = 143.0 with 61 - 2 = 59 degrees of freedom Variable Intercept Calcium Mortality (deaths/100,000) 2000 1800 1600 1400 1200+ Coefficient 1676 -3.23 30 SE(Coeff) 29.30 0.48 90 60 Calcium (ppm) 120 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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