In a survey of 2344 adults, 743 say they believe in UFOs. Construct a 95% confidence interval for the population proportion of adults who believe in UFOs.
A 95% confidence interval for the population proportion is (,)
Solution :
Given that,
n = 2344
x = 743
Point estimate = sample proportion = = x / n = 743 / 2344 = 0.317
1 - = 1 - 0.317 = 0.683
At 95% confidence level
= 1 - 95%
=1 - 0.95 =0.05
/2
= 0.025
Z/2
= Z0.025 = 1.960
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.96 (((0.317 * 0.683) / 2344 )
= 0.019
A 95% confidence interval for population proportion p is ,
± E
= 0.317 ± 0.019
= ( 0.298, 0.336 )
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