Question

Question 3 of 13 (1 point) A survey of 1050 U.S. adults found that 34% of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the 95% confidence interval of the true proportion. Round intermediate answers to at least five decimal places Round your final answers to three places ep

Answer 1

$\mathbf{given:}\;p=0.34,n=1050$

$\mathbf{for\; 95\%\; confidence \;level,\; z_{\frac{\alpha }{2}}=1.96}$

$\\\mathbf{formula:}\;Confidence\;Interval for Population \;proportion=\hat p \pm z_{\frac{\alpha }{2}}*\left \{ \sqrt{\frac{\hat p*(1-\hat p)}{n}} \right \}$

$=0.34 \pm 1.96*\left \{ \sqrt{\frac{0.34*(1-0.34)}{1050}} \right \}$

$=0.34 \pm 0.02865$

$Lower\;Bound=0.34 - 0.02865=0.31135\approx \mathbf{{\color{Red} 0.311}}$

$Upper\;Bound=0.34 +0.02865=0.36865\approx \mathbf{{\color{Red} 0.369}}$

$\mathbf{{\color{Red} 0.311}}<p< \mathbf{{\color{Red} 0.369}}$