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

No, not convinced that a majority of the voters oppose the bill.

Step-by-step solution

Given Information

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

Simplification

No, not convinced that a majority of the voters oppose the bill. This was a voluntary response sample. People who are strongly against this issue will take the time to write in. It is likely that the true proportion who oppose is less than $77\%$.