Question 6 An insurance comparny proposes two health insurance plans forthe empl

Question

Question 6 An insurance comparny proposes two health insurance plans forthe employees of company PlanA is the basic plan and covers only the medication expenses in case of hospitalization, whereas plan B reimburses all the medical expenses ofthe employes. As a human resources manager, you are required to estimate how many employees will opt for plan B. The manager randomly asks 50 Construct a 95% confidence interval estimate for the populationproportion ofemployees who Construct a 99% confidence interval estimate for thepopulationproportion ofemployees who Compare the results in (a) and (b) for different levels of confidence interval estimate for the employees and 17 of them prefer plan B. will prefer plan B. Interpret the results of the confidence interval. b) will prefer plan B. Interpret the results of the confidence interval c) population proportion of employees who will prefer plan B.

Explanation / Answer

a) ehre estimated proportion phat=17/50=0.34

for n=50 ; std error =(phat*(1-phat)/n)1/2 =0.067

for 95% confidence interval ; critial z value =1.96

therefore 95% confidence interval for population proportion =sample proportion-/+ z*std error

=0.2087 ; 0.4713

b)

for 99% confidence interval ; critial z value =2.5758

therefore 99% confidence interval for population proportion =sample proportion-/+ z*std error

=0.1674 ; 0.5124

c) we can see that as confidence level increases; width of confidence interval increases for 99% confidence level,

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