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 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) 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

Answers

Conditions for Normal approximation of Binomial probability:

Both np and np(1 - p) must be greater than 5, where n = sample size and p = population proportion.

Part (a)

Given p = 0.1, we should have 0.1n > 5 or n > 50 ……………………………(1)

And, 0.09n > 5 or n > 55 …………………………………………………………(2)

(1) and (2) => n > 55 => researcher should increase the sample size by at least 6. ANSWER

Part (b)

Given p = 0.15, we should have 0.15n > 5 or n > 33 ……………………………(1)

And, 0.1275n > 5 or n > 39 …………………………………………………………(2)

(1) and (2) => n > 39 => researcher should ask at least 40 persons => current sample size of 50 would suffice. ANSWER

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