Question

A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 50 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

Answer 1

Answer :

To assume.normality

N*p and n*p*(1-p) should be greater than or equal to 10

N = 50

a)

P = 0.15

N*p = 50*0.15 = 7.5

N*p*(1-p) = 50*0.15*0.85 = 6.375

Which is not greater than 10

N*0.15*0.85 = 10

N = 78

We have already 50 adults so the required number of additional adults are 78 - 50 = 28

That is 13 more adults should be sampled.

b)

P = 0.2

N*p = 50*0.2 = 10

N*p*(1-p) = 50*0.2*0.8 = 8

N*0.2*0.8 = 10

N = 63

We have already 50 adults so the required number of additional adults are 63 - 50 = 13

The researcher must ask 13 more americans adults.

Let me know in the comment section if anything is not clear. I will reply ASAP!

If you like the answer, please give a thumbs-up. This will be quite encouraging for me.Thank-you!