Question

A political-polling firm believes that the proportion of persons favoring a certain presidential policy is pi =.4. A sample of n = 100 persons is selected at random from the entire electorate, and the proportion favoring the presidential policy can be approximated by the normal distribution. If the actual parameter value is only pi =.37, what is the probability that 50% or more of the sample will favor the policy?

Answer 1

p =0.37

n=100

SE of proportion, SE = = = 0.05197

is estimated from sample.

P( 0.5) = P( ( - p) / SE (0.5 - 0.37)/ 0.05197) = P ( Z 2.50 ) = 1- P ( Z< 2.50 ) = 1- ( 2.5) = 1- .99379

= 0.0062

The probability that 50% or more of the sample will favor the policy ia 0.0062

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