Question

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10th of a percent)?

Answer 1

Answer:$\left ( 0.781,0.8175\right )$

Step-by-step explanation:

Given

Population Proportion $\left ( \hat{P}\right )$=$\frac{1600}{2000}$

$\hat{P}=0.8$

Confidence level =95 %

For 95% confidence interval level is $\hat{P} \pm \sqrt{\frac{\hat{P}\left ( 1-\hat{P}\right )}{n}}$

=$0.8\pm 1.96\sqrt{\frac{\hat{0.8}\left ( 1-\hat{0.8}\right )}{2000}}$

=$0.8\pm 1.96\times 8.94\times 10^{-3}$

The interval lies between $\left ( 0.781,0.8175\right )$