Question

For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent Mercer survey showed that 52% of U.S. employers were likely to require higher employee contributions for health care coverage. Suppose the survey was based on a sample of 400 companies. Compute the margin of error and a 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage. If required, round your answer to four decimal places. Round intermediate calculations to four decimal places.

Margin of Error:
Confidence Interval:	to

Answer 1

Given that,

Point estimate = sample proportion = = 0.52

Z_/2 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.52 * 0.48) / 400)

= 0.0490

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.52 - 0.0490 < p < 0.52 + 0.0490

0.4710 < p < 0.5690

Margin of error = 0.0490

Confidence interval : 0.4710 to 0.5690