14. A researcher studying public opinion of proposed Social Security changes obt

Question

14. A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 25 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases?

(a) 15% of all adult Americans support the changes

(b) 20% of all adult Americans support the changes

(a) The researcher must ask __?__ more American adults. (Round up to the nearest integer.)

(b) The researcher must ask __?__ more American adults. (Round up to the nearest integer.)

Explanation / Answer

To be approximately normal distribution, np > 5 and n(1-p) > 5

a) p = 0.15

np > 5

or, n * 0.15 > 5

or, n > 33.33

or, n = 34

34 - 25 = 9

The researcher must ask __9__ more American adults

b)

p = 0.2

np > 5

or, n * 0.2 > 5

or, n > 25

or, n = 25

25 - 25 = 0

The researcher must ask __0__ more American adults

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