Question

3 pts A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 30 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 if 45% of all adult American support the changes? 11 pos Question 16 8 %

Answer 1

$\\ $ 45\% of all american adults support the changes $ \\\\ $ So, population proportion$(p) = 0.45 \\\\ $ Let sample size needed be $ "n" \\\\ $ For distribution of sample proportion to be normal $ \\\\ np(1-p) \geq 10 \\\\ \Rightarrow n * 0.45 * (1-0.45) \geq 10 \\\\ \Rightarrow n \geq \frac{10}{0.45 * 0.55} \\\\ \Rightarrow n \geq 40.40 \\\\ $ So, minimum sample size needed is $ 41 \\\\ $ 30 adults are already sampled $ \\\\ $ Thus, additional adults needed to sample $ = 41 - 30 = \mathbf{11}$