Question

A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adults Americans and asks them wether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is apporoximately normal, how many more adult Americans does the researcher need to sample in the following cases?

(a) 10% of all adult Anericans support the changes

(b) 15% of all adults Americans support the changes

Answer 1

a) Here, p = 0.1, so q = 1-p = 1-0.1 = 0.9.

So, in order to make the distribution of the people who say yes, approximately normal, the following condition need to be satisfied:

n* p * q > = 10

n * 0.1 * 0.9 > = 10

0.09* n > = 10

n >= 111.11,

So, n should be greater than equal to 112, in order to make the distribution approximately normal.

b)

Here, p = 0.15, so q = 1-p = 1-0.15 = 0.85.

So, in order to make the distribution of the people who say yes, approximately normal, the following condition need to be satisfied:

n* p * q > = 10

n * 0.15 * 0.85 > = 10

0.1275* n > = 10

n > = 78.43,

So, n should be greater than equal to 79, in order to make the distribution approximately normal.

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