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

Explanation / Answer

Ans:

For distribution to be normal,it must follow rule of sample proportions:

np>=10

n(1-p)>=10

Now,in above problem,n=30

a)p=0.1

np=30*0.1=3

but it should be atleast 10

if n=100

np=100*0.1=10

So,they should sample atleast 100 adults,it means they need 70 more sdults to sample( i.e.30+70=100)

b)now when p=0.15

np=30*0.15=4.5

if n=67

np=67*0.15=10.05

Hence,atleast 67 adults are needed to sample,so 67-30=47 more dults are needed.

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