Question

It is said that happy and healthy workers are efficient and productive. A researcher wants to know the percentage of large companies that provide on-site health club facilities. A sample of 240 such companies showed that about 96 of them provide such facilities on site. a. What is the point estimate of the percentage of all such companies that provide such facilities on site? The point estimate is 0.40 in decimal form. b. Find a 95% confidence interval for the corresponding population proportion. Round to THREE decimal places this time. The confidence interval for the proportion is between 0.338 and 0.462 . c. What is the margin of error associated with this interval? Round to THREE decimal places. (Hint: it is half of the width of the confidence interval.)

Answer 1

$a.~a. ~The~ point ~estimate~ of ~the~ percentage~ of ~all~ such ~companies ~that~ provide\\ ~ such~ facilities~ on ~site=\hat{p}=96/240=0.4 0\\ b.~95\%~C.I.~for~corresponding~population~proportion:\\ \left[\hat{p}-Z_{0.025}\sqrt{\frac{\hat{p}(1-\hat{p})}{240}},~\hat{p}+Z_{0.025}\sqrt{\frac{\hat{p}(1-\hat{p})}{240}} \right ]=[0.338,~0.462]\\ where,~Z_{0.025}=1.96\\ c.~Margin~of~error=Z_{0.025}\sqrt{\frac{\hat{p}(1-\hat{p})}{240}}=0.062$