In a survey of 652 males ages 18-64, 392 say they have gone to the dentist in th
ID: 3208473 • Letter: I
Question
In a survey of 652 males ages 18-64, 392 say they have gone to the dentist in the post year. Construct 90% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. The 90% confidence intervals for the population proportion p is (). The 95% confidence interval for the population proportion p is (). Interpret you results of both confidence intervals. A. 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 a interval. B. 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 a interval. C. With the given confidence, it can be said that the population proportion of male ages 18-64 who say they have gone to the dentist is the pasty year is not between the endpoints of the given confidence interval. Which interval is wider? The 90% confidence interval The 95% confidence interval.Explanation / Answer
a.
p = 392/652 = .6
The confidence iterval is got by formula
= p +/- Z*Sqrt(p*(1-p)/n)
For 90% the Z value is 1.645
= .6+/- 1.645*sqrt(.6*.4/652)
=.57 to .63
For 95% the Z value is 1.96
= .6+/- 1.96*sqrt(.6*.4/652)
=.56 to .64
b.
A is the right interpretation. Remember the confidence interval is for:
1. population proportion - B elimnated
2. It says population parameter is between the 2 end points - C eliminated
c.
95% interval is wider, as you can see .56 to .64 is wider than .57 to .63
This is becuase if u want more confidence of population proportion, then you have to strench your interval and say more "confidently" that the pop. param is within this range.
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