Question

8.2.23 Question Help 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 charges. 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)

Answer 1

Answer:

a)

Given,

p = 0.1

consider,

np(1-p) >= 10

n(0.1)(1-0.1) = 10

n*0.1*0.9 = 10

n*0.09 = 10

n = 10/0.09

n = 111

We have already 50 adults , so the required number of adults are 111 - 50 = 61

b)

p = 0.15

np(1-p) >= 10

n*0.15(1-0.15) = 10

n*0.15*0.85 = 10

n *0.1275 = 10

n = 78.43

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