Question 1044004: In a survey of 628 males ages 18-64, 393 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? 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 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.
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 interval.
C.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.
Which interval is wider?
a)The 90% confidence interval
b)The 95% confidence interval
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! proportion(p) = 393 / 628 = 0.6258
:
standard error(se) = square root( 0.6258 * (1-0.6258) / 628 ) = 0.0193
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90% confidence interval(CI)
:
alpha(a) = 1 - (90/100) = 0.10
critical probability(p*) = 1 - (0.10/2) = 0.95
degrees of freedom(df) = 628 -1 = 627
critical value(use t statistic calculator) = 1.647
margin of error(me) = 1.647 * 0.0193 = 0.0318
90% ci is 0.626 + or - 0.032, that is, (0.594, 0.658)
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95% ci
:
a = 1 - (95/100) = 0.05
p* = 1 - (0.05/2) = 0.975
df = 627
cv = 1.964
me = 1.964 * 0.0193 = 0.0379
95% ci is 0.626 + or - 0.038, that is, (0.588, 0.664)
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90% ci is (0.594, 0.658)
95% ci is (0.588, 0.664)
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We are trying to estimate the population proportion, answer is B
95% ci is wider, answer is b
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