In a survey of 644 mates ages 18-64, 3999 say they have gone, o the dent*, in th

Question

In a survey of 644 mates ages 18-64, 3999 say they have gone, o the dent*, in the pas. Year construct 90% and 95% confidence intervals for the population proportion, Intercept the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. The 90% coefficients interval for the population proportion p is () The 95% confidence interval for the population proportion p is () Interpret your results of both confidence intervals. With the given confidence, it can be said that the population proportion of males ages 18-64 Who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval With the given confidence, it can be said that the population proportion of males ages 18-64 Who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval With the given confidence, it can be said that the population proportion of males ages 18-64 Who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval The 90% confidence interval

Explanation / Answer

Here p^=399/644=0.62

Now for se=sqrt(p(1-p)/n)=0.02

For 90% z=1.645 and for 95% z=1.96

Now E for 90%=z*se=0.0329 and for 95% E=0.0392.

Hence CI for 90%=p+/-E=0.62+/-0.0329=(0.587,0.6529)

For 95% CI=(0.581,0.659)

CI give population proportions between end points so A is correct.

We can see that 95% CI is wider

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