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.

Solution

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.

From Solvely APP
Source: https://solvelyapp.com/problems/AeBdb7LvYu/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download