a researcher studying public opinion of proposed social security changes obtains a simple random sample of…

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 \\( \\hat { p } \\), 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 adult americans support the changes (a) the researcher must ask \\( \\square \\) more american adults. (round up to the nearest integer.)

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 \\( \\hat { p } \\), 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 adult americans support the changes (a) the researcher must ask \\( \\square \\) more american adults. (round up to the nearest integer.)

Answer

Explanation:

Step1: Recall the normal - approximation condition for the sampling distribution of (\hat{p})

The sampling distribution of (\hat{p}) is approximately normal if (np\geq10) and (n(1 - p)\geq10), where (n) is the sample size and (p) is the population proportion.

Step2: For part (a) with (p = 0.2)

Let (n) be the sample size. We need (np\geq10) and (n(1 - p)\geq10). Substituting (p = 0.2) into (np\geq10), we get (n\times0.2\geq10), so (n\geq\frac{10}{0.2}=50). Since the current sample size (n_0 = 30), the number of additional people (n - n_0=50 - 30 = 20).

Answer:

20