A simple random sample of $1200$ adult Americans is selected, and each person is asked the following question: “In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?” Only $39\%$ of those responding answered “Yes.” This survey

(a) is reasonably accurate since it used a large simple random sample.

(b) needs to be larger since only about $24$ people were drawn from each state.

(c) probably understates the percent of people who favor a system of national health insurance.

(d) is very inaccurate but neither understates nor overstates the percent of people who favor a system of national health insurance. Since simple random sampling was used, it is unbiased.

(e) probably overstates the percent of people who favor a system of national health insurance.

Step by step solution

01

Given information

Number of adult Americans, $n=1200$
We have to find the best statement regarding this survey.

02

Concept

A simple random sample (SRS) of size $n$ is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

03

Explanation

Each person is chosen at random and asked if, in view of the massive national deficit, the government should spend more money now to build a national health insurance system. Option (c) is thus the correct option because the question promotes bias responses and will most likely result in an underestimating by providing the respondent with more information that may impact their answer. As a result, the percentage of respondents who support a national health-care system is likely underestimated in this poll.

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