Question

Volkswagen emissions scandal. Refer to the Significance (December 2015) study on estimating the number of U.S. deaths attributable to nitrogen oxide (NOx) pollution produced from illegal VW vehicles, Exercise 2.30 (p. 85). Recall that the researchers computed the estimate for each of 27 different scenarios involving different values of three variables: total distance (in miles) driven by these illegal VW vehicles, the amount by which the VW vehicles exceeded the EPA standard for NOx, and the estimated association between NOx emissions and mortality. The data (simulated from results reported in the study) are reproduced in the accompanying table. Assume that one of the 27 scenarios did occur and that the estimate for this scenario represents the actual number of deaths. Give an interval that will likely contain the number of deaths attributable to NOx pollution over the 7 years.

Short answer

$\text{CI =}\left(73.49,253.99\right)$

Step-by-step solution

Pollution

Pollution is the release of hazardous pollutants into the ecosystem. These hazardous elements are referred to as contaminants. Pollutants may be naturally occurring, including such volcanic ash. They can also be due to human activities, including such factory runoff as well as waste.

Explanation

Let X be the total number of fatalities in the sample.

$$\begin{gathered} \stackrel{-}{X}=163.44 \\ S=227.38 \\ n=27 \\ \text{95\% confidence interval} \\ \text{CI =}\overline{X}\pm T_{\frac{\alpha }{2}}\left(\frac{S}{\sqrt{n}}\right) \end{gathered}$$

$\text{Degree of freedom = n}-\text{1 = 26}$

For 95% confidence $T_{\frac{\alpha }{2}}=2.0555$

$$\begin{gathered} \text{CI}=163.44\pm 2.0555\left(\frac{227.38}{\sqrt{27}}\right) \\ \text{CI = 163.44}\pm 89.95 \\ \text{CI =}\left(73.49,253.99\right) \end{gathered}$$