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bearhunter [10]
3 years ago
10

A Rasmussen Reports survey of 1,000 US adults found that 42% believe raising the minimum wage will help the economy. Construct a

99% confidence interval for the true proportion of US adults who believe this.
Mathematics
1 answer:
vitfil [10]3 years ago
6 0

Answer:

(0.3798, 0.4602)

Step-by-step explanation:

Let p be the true proportion of US adults who believe raising the minimum wage will help the economy. A point estimate for p is \hat{p}=0.42 and a good aproximation (because we have a large sample) for the standard deviation of \hat{p} is \sqrt{\hat{p}(1-\hat{p})/n}=\sqrt{0.42(0.58)/1000}=0.0156. Therefore, a 99% confidence interval for p is given by \hat{p}\pm z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} where \alpha=0.01 and z_{\alpha/2} is the \alpha/2th quantile of the standard normal distribution, so we have, 0.42\pm z_{0.005}0.0156, i.e., 0.42\pm(-2.5758)(0.0156) or equivalently (0.3798, 0.4602).

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