Mathematics, 15.04.2020 02:10 njorda7211
In a survey of 2148 adults in a recent year, 1352 say they have made a New Year's resolution. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
Answers: 3
![CI_{90\%}=[0.6123,\ 0.6465]\\\\CI_{95\%}=[0.6090,\ 0.6498]](/tpl/images/0600/7680/af993.png)
as follows:
![CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=0.6294\pm 1.645\times \sqrt{\frac{0.6294(1-0.6294)}{2148}}\\\\=0.6294\pm0.0171\\\\=[0.6123,\ 0.6465]](/tpl/images/0600/7680/fe603.png)
![CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=0.6294\pm 1.96\times \sqrt{\frac{0.6294(1-0.6294)}{2148}}\\\\=0.6294\pm0.0204\\\\=[0.6090,\ 0.6498]](/tpl/images/0600/7680/90e3e.png)
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In a survey of 2148 adults in a recent year, 1352 say they have made a New Year's resolution. Constr...
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