Apollster wants to construct a 95% confidence interval for the proportion of adults who believe that economic conditions are getting better. a gallup poll taken in july 2010 estimates this proportion to be 0.33. using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.052 ?

The sample size of 315 is needed so that the confidence interval will have a margin of error of 0.052 .

Step-by-step explanation:

The Margin of error for population proportion is given by :-

Given : Significance level :

     [By standard normal distribution table]

Proportion of adults who believe that economic conditions are getting better : p=0.33.

Margin of error : E= 0.052

Substitute all the value in the above formula, we get

Squaring both sides , we get

Hence, the required sample size = 315

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the answer is 0.3175 hope that you ^w^

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