Example 18

EXAMPLE 18 Americans’ Concern About Climate Change

Are Americans concerned about climate change, and if so, what would they be willing to sacrifice? in 2014, the Bloomberg National Poll surveyed 1005 U.S. adults on climate change and other topics. Of those surveyed:

462 viewed climate change as a major threat.
623 indicated that they would be willing to pay more for energy if air pollution from carbon emissions could be reduced.

Powers and Roots

The sample proportion who viewed climate change as a major threat is

$\hat{p} = \frac{462}{1005} \approx 0.4597$

A 95% confidence interval for the proportion $p$ of all U.S. adults who view climate change as a major threat is

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$\begin{matrix} \hat{p} \pm 2 \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}} = 0.4597 \pm 2 \sqrt{\frac{(0.4597) (0.5403)}{1005}} \\ \begin{matrix} = 0.4597 \pm 0.0314 & or & 45.97 % \pm 3.14 % \\ = 0.4283 to 0.4911 & or & 42.83 % to 49.11 % \end{matrix} \end{matrix}$

A report of these calculations might say, “The study found that approximately 46% of U.S. adults viewed climate change as a major threat. The margin of error for this result is 3.1%.”