In a survey of 644 males ages 18-64, 395 say they have gone to the dentist in th
ID: 3200555 • Letter: I
Question
In a survey of 644 males ages 18-64, 395 say they have gone to the dentist in the past year. Construct 90% and 95% 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 interval for the population proportion p is (n___,___). (Round to three decimal places as needed.)
The 95% confidence interval for the population proportion p is (___,___). (Round to three decimal places as needed.)
Interpret your 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 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 not between the endpoints of the given confidence interval.
C. With the given confidence, it can be said that the sample 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.
Which interval is wider?
The 90% confidence interval
The 95% confidence interval
Explanation / Answer
Proportion (p) = 395 / 644 = 0.6133
standard error(se) = square root(0.6133* (1-0.6133) / 644 )
= 0.01919
90% confidence interval( CI) :
alpha(a) = 1 - (90/100) = 0.10
critical probability(p*) = 1 - (0.10/2) = 0.95
degrees of freedom(df) = 644-1 = 643
critical value(use t statistic calculator) = 1.647
margin of error(me) = 1.647 * 0.01919= 0.03160
90% CI is 0.613 + or - 0.032, that is, (0.581, 0.645)
95% Confidence Interval (CI) :
alpha(a) = 1 - (95/100) = 0.05
critical probability(p*) = 1 - (0.05/2) = 0.975
degrees of freedom(df) = 643
critical value(use t statistic calculator) = 1.964
margin of error(me) = 1.964 * 0.01919= 0.0377
95% CI is 0.613 + or - 0.038, that is, (0.575, 0.651)
90% CI is (0.581, 0.645)
95% CI is (0.575, 0.651)
We are trying to estimate the population proportion, answer is B
With the 95% 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 not between the endpoints of the given confidence interval.
The 95% confidence interval is wider.
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