Question

In: Statistics and Probability

7. A political group randomly samples 60 potential voters to gauge the proportion of voters who...

7. A political group randomly samples 60 potential voters to gauge the proportion of voters who favor a certain legislative issue. Assume the true proportion of voters who favor the issue is 75%. Find the probability that the sample fraction who favor the legislation will be within 0.10 of the true fraction.

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Expert Solution

Solution:

Given:

Sample size = n = 60

The true proportion of voters who favor the issue is 75%.

Thus p = 0.75

We have to find the probability that  the sample fraction who favor the legislation will be within 0.10 of the true fraction.

That is find:

Look in z table for z = 1.7 and 0.09 as well as for z = -1.7 and 0.09 and find corresponding area.

P( Z< -1.79) = 0.0367

and

P(Z < 1.79 ) = 0.9633

thus

The probability that the sample fraction who favor the legislation will be within 0.10 of the true fraction 0.9266

orchestra answered 1 year ago
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