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A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 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 researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 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) 20% of all adult Americans support the changes(b) 25% of all adults Americans support the changes
Final answer:To determine the number of adult Americans needed for the distribution of thesampleproportion to be approximately normal, we can use the formula n = (Z/E)^2 * p * (1-p).Explanation:To determine the number of adult Americans needed for the distribution of the sampleproportionto be approximately normal, we need to calculate the minimum sample size n required. We can use the formula:n = (Z₃/E)^2 * p * (1-p)Where Z₃ is the critical value, E is the maximum error tolerance (which is half the width of the confidence interval), and p is the estimated proportion of adult Americans who support the changes.For part (a), where 20% of all adult Americans support the changes, the estimated proportion p is 0.20. Plugging in the values for Z₃ and E, we can solve for n. Similarly, for part (b), where 25% of all adult Americans support the changes, the estimated proportion p is 0.25. Plugging in the values for Z₃ and E, we can solve for n.Learn more about Sample Proportion here:brainly.com/question/32638029#SPJ2...