How's the economy? A pollster wants to construct a 99.5%
confidence interval for the proportion of
adults who believe that economic conditions are getting better.
b) Estimate the sample size needed if no estimate of P is available.
A sample of _ adults is needed to obtain a 99.5 confidence interval with a margin of error of 0.03.
Solution,
Given that,
= 1 -
= 0.5
margin of error = E = 0.03
At 99.5% confidence level
= 1 - 99.5%
= 1 - 0.99.5 =0.005
/2
= 0.0025
Z/2
= Z0.0025 = 2.807
sample size = n = (Z / 2 / E )2 *
* (1 -
)
= (2.807 / 0.03 )2 * 0.5 * 0.5
= 2188.68
sample size = n = 2189
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