A researcher studying public opinion of proposed Social Security changes obtains

Question

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? 15% of all adult Americans support the changes 20% of all adult Americans support the changes The researcher must ask more American adults. (Round up to the nearest integer.) The researcher must ask more American adults. (Round up to the nearest integer.)

Explanation / Answer

In general, the distribution of a binomial random variable may be accurately approximated by that of a normal random variable, as long as np 5, nq 5,

a)

p = 0.15

np>=5

n>=33.33

n>=34

Researcher must ask 9 more american adults

b)

np>=5

p = 0.20

n>=25

n>=25

So the reseacrher must ask zero more american adults

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