Lead is toxic, particularly for young children, and for this
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Lead is toxic, particularly for young children, and for this reason government regulations severely restrict the amount
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Lead is toxic, particularly for young children, and for this reason government regulations severely restrict the amount of lead in our environment. But this was not always the case. In the early part of the 20th century, the underground water pipes in many U.S. cities contained lead, and lead from these pipes leached into drinking water. In this exercise you will investigate the effect of these lead water pipes on infant mortality. On the text website www.pearsonglobaleditions.com/Stock_Watson, you will find the data file Lead_Mortality, which contains data on infant mortality, type of water pipes (lead or non-lead), water acidity (pH), and several demographic variables for 172 U.S. cities in 1900.5 A detailed description is given in Lead_Mortality_ Description, also available on the website. a. Compute the average infant mortality rate (Inf ) for cities with lead pipes and for cities with non-lead pipes. Is there a statistically significant difference in the averages? b. The amount of lead leached from lead pipes depends on the chemistry of the water running through the pipes. The more acidic the water (that is, the lower its pH), the more lead is leached. Run a regression of Inf on Lead, pH, and the interaction term Lead * pH. i. The regression includes four coefficients (the intercept and the three coefficients multiplying the regressors). Explain what each coefficient measures. ii. Plot the estimated regression function relating Inf to pH for Lead = 0 and for Lead = 1. Describe the differences in the regression functions and relate these differences to the coefficients you discussed in (i). iii. Does Lead have a statistically significant effect on infant mortality? Explain. iv. Does the effect of Lead on infant mortality depend on pH? Is this dependence statistically significant? v. What is the average value of pH in the sample? At this pH level, what is the estimated effect of Lead on infant mortality? What is the standard deviation of pH? Suppose that the pH level is one standard deviation lower than the average level of pH in the sample; what is the estimated effect of Lead on infant mortality? What if pH is one standard deviation higher than the average value? vi. Construct a 95% confidence interval for the effect of Lead on infant mortality when pH = 6.5. c. The analysis in (b) may suffer from omitted variable bias because it neglects factors that affect infant mortality and that might potentially be correlated with Lead and pH. Investigate this concern, using the other variables in the data set.
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