A population proportion is to be estimated from the sample described. Approximate the 95% confidence interval. Round your answer to four decimal places, if necessary.
-A researcher wishes to estimate the proportion of left handed people among a certain population. In a random sample of 1000 people from the population, $61.9 \%$ are left-handed. Find the $95 \%$ confidence interval for the population proportion of left-handed people.
A) $0.5973

Question

A population proportion is to be estimated from the sample described. Approximate the 95% confidence interval. Round your answer to four decimal places, if necessary.
-A researcher wishes to estimate the proportion of left handed people among a certain population. In a random sample of 1000 people from the population, $61.9 \%$ are left-handed. Find the $95 \%$ confidence interval for the population proportion of left-handed people.
A) $0.5973 < \mathrm { p } < 0.6407$
B) $0.5874 < \mathrm { p } < 0.6506$
C) $0.6180 < \mathrm { p } < 0.6200$
D) $0.5883 < \mathrm { p } < 0.6497$

Quizplus · Accepted Answer

The 95% confidence interval for the population proportion is calculated using the formula: $\hat{p} \pm z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p} = 0.619$, $z = 1.96$ for 95% confidence, and $n = 1000$. Plugging these values in gives the interval $0.5883 < p < 0.6497$.

A Population Proportion Is to Be Estimated from the Sample 61.9%61.9 \%61.9%

A Population Proportion Is to Be Estimated from the Sample $61.9 \%$