91Ó°ÊÓ

The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal, Of these, 89 say "Yes."

The formula to compute the confidence interval for population proportion is:

$CI=\hat{p}Â\pm z_{\mathrm{Î\pm }/2}×\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Here,

$\text{Number of trials}\left(n\right)=150$

$\text{Number of events}\left(x\right)=89$

The obtained Minitab output is:

Therefore,

There is $99\%$probability that the proportion of visitors who are favor of restrictions lies between $0.485$and $0.696$

The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal, Of these, 89 say "Yes."

The confidence interval computed in above part lies between $0.486$and $0.696$. Since, it contains the value (0.50) and upper limit of the confidence interval is higher than $0.50$. Thus, it could be concluded that more than half of visitors are favor of restriction.