6. Explain it to the congresswoman You are on the staff of a member of Congress

Question

6. 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?

Explanation / Answer

No, based on the given data of 871 out of 1128 are opposing the legislation, I am not convinced that a majority of the voters oppose the bill. Because, this sample proportion 0.77 = 871/1128 of the fraction of people opposing the bill, is obtained by assuming that the sample of 1128 received letters is actually sufficiently representative of the entire population of constituency. However, this assumption is not valid because it may be the case that the sample of 1128 received letters consists of mostly only those people from the constituency who are against the bill. But we don't know about the people from whom no letters were received. We can't assume that they are in opposition of the bill. So, this is the issue of whether or not the sample collected is unbiased and sufficiently representative of true population or not. And this is the way in which we can explain this issue to congresswoman.

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