Question
In: Statistics and Probability
In a survey of 609609 males ages 18-64, 397397 say they have gone to the dentist...
In a survey of
609609
males ages 18-64,
397397
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
(nothing,nothing).
(Round to three decimal places as needed.)
Solutions
Expert Solution
Sample proportion 
= 397 / 609
= 0.652
90% confidence interval for p is
- z * sqrt(
( 1 -
) / n) <
p < + z * sqrt(
( 1 -
) / n)
0.652 - 1.645 * sqrt( 0.652 * ( 1 - 0.652) / 609) < p < 0.652 + 1.645 * sqrt( 0.652 * ( 1 - 0.652) / 609)
0.620 < p < 0.684
90% CI is ( 0.620 , 0.684 )
Interpretation - We are 90% confident that population proportion of males who say they have
gone to the dentist in the past year is between 0.620 and 0.684
95% confidence interval for p is
- z * sqrt(
( 1 -
) / n) <
p < + z * sqrt(
( 1 -
) /
n)
0.652 - 1.96 * sqrt( 0.652 * ( 1 - 0.652) / 609) < p < 0.652 + 1.96 * sqrt( 0.652 * ( 1 - 0.652) / 609)
0.614 < p < 0.690
95% CI is ( 0.614 , 0.690 )
Interpretation - We are 95% confident that population proportion of males who say they have
gone to the dentist in the past year is between 0.614 and 0.690
Comparison = 95% confidence interval is wider than 90% confidence interval.
orchestra answered 1 year agoRelated Solutions
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