Stat 10 Chattey Fal 2017 Homework: Homework #11 core: 0 of 1 pt 5of8(a complete)

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Stat 10 Chattey Fal 2017 Homework: Homework #11 core: 0 of 1 pt 5of8(a complete) HN Score: 60%, 4 80 38.2.23 Question Help A researcher shudying public opinion of proposed Social Sacurily changes obtains a simple random sample of 50 adut Americans and asks thom whether or not Americans does the rosearcher need to sample in the following cases? (a) 19% of aE adult Americans support the changes propeonien of bdas whoesapme a (b) 20% of al aalt Americans support the changes (a) The researcher must ask more American adults. (Round up to the nearest integer.) w bos and then cick Checs Answer

Explanation / Answer

In order of approximate the Binomial probability with Normal one, we should have n > 30, np > 10 and n(1-p) > 10.

a) Here, given that p = 0.15

Thus, if np > 10, then 0.15n > 10 i.e n > 66.67.....(i)....

Also, if n(1 -p) > 10, then, 0.85n > 10 i.e n > 11.76....(ii)....

Combining, (i) and (ii) we have, n should be at least 67.

Hence, we need to draw (67-50) = 17 more samples.

b) Given that, p = 0.2

Thus, if np > 10, we have, 0.2n > 10 i.e. n > 50....(iii)....

If n(1 - p) > 10, we have, 0.8n > 10 i.e n > 12.5....(iv)....

Combining (iii) and (iv) we have, n should be atleast 51.

Thus, we need to draw (51 - 50) = 1 more sample. (Ans).

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