Question

Explain it to the congresswoman You are on the staff of a member of Congress who is considering a bill that would provide government-sponsored insurance for nursing-home care. You report that $1128$ letters have been received on the issue, of which $871$ oppose the legislation. “I’m surprised that most of my constituents oppose the bill. I thought it would be quite popular,” says the congresswoman. Are you convinced that a majority of the voters oppose the bill? How would you explain the statistical issue to the congresswoman?

Short answer

The percentage of letters opposing the insurance should not be seen as an accurate representation of the congresswoman's constituents' views. Only those with strong opinions will submit a letter.

Step-by-step solution

Given information

$1128$ letters for government-sponsored nursing-home care insurance have been received. Because the majority of people oppose the bill, we must explain to the congresswoman whether we are confident that a majority of voters oppose the law and the statistical issue.

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.

Explanation

Voluntary response sampling is demonstrated by letters to legislators. People decide whether or not to join the sample in response to an open invitation in involuntary response sampling, which is virtually always biassed. Voluntary response samples draw people who are passionate about the topic, resulting in bias. The sample is biased since it does not represent the entire population; rather, it represents a subset of the population with strong opinions. As a result, the percentage of letters opposing the insurance should not be taken as an accurate representation of the congresswoman's constituents' views. Only those with strong opinions will submit a letter.