Question

The Terri Schiavo Case. In the early part of 2005, the Terri Schiavo case received national attention as her husband sought to have life support removed, and her parents sought to maintain that life support. The courts allowed the life support to be removed, and her death ensued. A Harris Poll of 1010 U.S. adults was taken by telephone on April 21, 2005, to determine how common it is for life support systems to be removed. Those questioned in the sample were asked: (1) Has one of your parents, a close friend, or a family member died in the last 10 years? (2) Before (this death/these deaths) happened, was this person/were any of these people, kept alive by any support system? (3) Did this person die while on a life support system, or had it been withdrawn? Respondents were also asked questions about age, sex, race, education, region, and household income to ensure that results represented a cross-section of U.S. adults.

(a) What kind of sampling design was used in this survey? Explain your answer

(b) If 78% of the respondents answered the first question in the affirmative, what was the approximate sample size for the second question?

(c) If 28% of those responding to the second question answered "yes," what was the approximate sample size for the third question?

Short answer

Part (a) Simple random sample

Part (b)$\approx 788$

Part (c)$\approx 221$

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

A Harris Poll of 1010 U.S. adults was taken by telephone on April 21, 2005, to determine how common it is for life support systems to be removed. Those questioned in the sample were asked:

(1) Has one of your parents, a close friend, or a family member died in the last 10 years?

(2) Before (this death/these deaths) happened, was this person/were any of these people, kept alive by any support system?

(3) Did this person die while on a life support system, or had it been withdrawn?

Respondents were also asked questions about age, sex, race, education, region, and household income to ensure that results represented a cross-section of U.S. adults.

Part (a) Step 2. State which type of sampling design was used in this survey.

Because 1010 were taken by phone on April 21, 2005, to ascertain about the life support systems, the sampling design utilized was a "simple random sample."

That is, the sampled phone numbers are chosen at random.

Part (b) Step 1. The approximate sample size for the second question if 78% of the respondents answered the first question in the affirmative.

In this case, 78 percent of 1010 members say yes to the first question, indicating that some members had died in the recent ten years.

As a result, for the second question, the sample size is determined as follows.$$\begin{gathered} =1010(78\%) \\ =\frac{1010}{100}\times 78 \\ =787.8788 \\ \approx 788 \end{gathered}$$

Part (c) Step 1. The approximate sample size for the third question.

We are provided that 28 percent of answers to the second question believe that the deceased person was kept alive by any life-support system before death.

As a result, for the second question, the sample size is determined as follows:

$$\begin{gathered} =788(28\%) \\ =220.64 \\ \approx 221 \end{gathered}$$