Problem

A survey of 2288 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 428 have donated blood in the past two years. Complete parts (a) through (c) below.
(a) Obtain a point estimate for the population proportion of adults in the country aged 18 and older who have donated blood in the past two years.
\[
\hat{p}=0.187
\]
(Round to three decimal places as needed.)
(b) Verify that the requirements for constructing a confidence interval about $p$ are satisfied.

Answer

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Answer

Therefore, the requirements for constructing a confidence interval about \(p\) are satisfied.

Steps

Step 1 :The point estimate for the population proportion of adults who have donated blood in the past two years is \(\hat{p}=0.187\).

Step 2 :To verify the requirements for constructing a confidence interval about \(p\), we check if the conditions are satisfied:

Step 3 :1. Random Sample: The survey was conducted on 2288 adults, which can be considered a random sample.

Step 4 :2. Independence: It is assumed that the responses of one adult do not influence the responses of another adult in the survey.

Step 5 :3. Sample Size: The sample size of 2288 is sufficiently large for the normal approximation to be valid. Both \(np\) and \(n(1-p)\) should be greater than 10, where \(n\) is the sample size and \(p\) is the estimated proportion. In this case, \(2288 \times 0.187 \approx 428\) and \(2288 \times (1-0.187) \approx 1860\), both of which are greater than 10.

Step 6 :Therefore, the requirements for constructing a confidence interval about \(p\) are satisfied.

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