Chapter 4.1, Problem 9E

To determine

To find out that are you convinced that the majority of the voters oppose the bill or not and also how would you explain the statistical issue to the congress woman.

Answer to Problem 9E

No.

Explanation of Solution

No, we are not convinced that a majority of the voters oppose the bill, as based on the data of $871$ out of $1128$ are opposing the legislation.

Because this sample proportion is,

  $\frac{871}{1128}=0.77$

  $0.77$ of the fraction of people opposing the bill is obtained by assuming that the sample of $1128$ received letters is actually representative of the entire population of constituency. However, this assumption is not valid because it may be the case that the sample of $1128$ people consist of mostly only those people from the constituency those are against the bill. But we do not know about the people from whom no letters are received. We cannot assume that they are against the bill. So, this is the issue of whether or not the sample collected is unbiased and sufficiently representative of the true population or not. And this is the way in which we can explain the congress woman.