Question

Organ Donors USA Today provided information about a survey (conducted for Donate Life America) of 5100 adult Internet users. Of the respondents, 2346 said they are willing to donate organs after death. In this survey, 100 adults were surveyed in each state and the District of Columbia, and results were weighted to account for the different state population sizes.

a. What percentage of respondents said that they are willing to donate organs after death?

b. Based on the poll results, what is the probability of randomly selecting an adult who is willing to donate organs after death?

c. What term is used to describe the sampling method of randomly selecting 100 adults from each state and the District of Columbia?

Short answer

a. The percentage of respondents that are willing to donate their organs after death is equal to 46%.

b. The probability of selecting an adult who is willing to donate organs after death is equal to 0.460.

c. The term used to describe the method of sampling in which 100 adults are randomly selected from each state and District of Columbia is “Stratified Random Sampling.”

Step-by-step solution

Given information

In a survey, 2346 adults out of 5100 adults said they were willing to donate their organs after death.

One hundred adults were randomly selected from each state and the District of Columbia.

Compute the percentage

a.

The percentage of respondents who were willing to donate organs is computed below:

$$\begin{gathered} \text{Percentage}=\frac{\text{Number}\text{of}\text{respondents}\text{who}\text{were}\text{willing}\text{to}\text{donate}\text{organs}}{\text{Total}\text{number}\text{of}\text{respondents}}\times 100 \\ =\frac{2346}{5100}\times 100 \\ =46\% \end{gathered}$$

Therefore, the percentage of respondents willing to donate organs is 46%.

Compute the probability

b.

Probability measures the chances of appearance of an event in a feasible number of outcomes.

Let A be the event of selecting a respondent who is willing to donate organs after death.

The probability value is obtained as follows:

$$\begin{gathered} P\left(A\right)=\frac{\text{Number}\text{of}\text{respondents}\text{who}\text{were}\text{willing}\text{to}\text{donate}\text{organs}}{\text{Total}\text{number}\text{of}\text{respondents}} \\ =\frac{2346}{5100} \\ =0.460 \end{gathered}$$

Therefore, the probability of selecting a respondent who is willing to donate organs is equal to 0.460.

Express the method of sampling

c.

When the total number of units in the entire population isdivided into strata, and samples of fixed sizes are chosen from each stratum, it is called the stratified random sampling method.

Here, the entire adult population is divided into the states and the District of Columbia.

These states and the District of Columbia are the strata. Moreover, samples of size 100 are selected from each stratum to conduct the survey.

Thus, the method of sampling used is stratified random sampling.