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 30 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? 10% of all adult Americans support the changes 15% of all adult Americans support the changes The researcher must ask 82 more American adults. (Round up to the nearest integer.) The researcher must ask more American adults. (Round up to the nearest integer.)

Explanation / Answer

Solutiona:

Given normal distr

np(1-p)>=10
solve np(1-p)=10

n(0.1)(1-0.1)=10

n(0.1)(0.9)=10

n(0.09)=10

n=111.11

n=111

we have already 30

so

111-30=81

81 needed more

SOlutionb:

we have np(1-p)>=10

n(0.15)(1-0.15)>=10

n(0.15)(0.85)=10

n(0.1275)=10

n=10/0.1275

n=78.43

n=78

already we have 30

s0 78-30=48 needed

ANSWER 48

ANSWERS

(A)81

(B)=48

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