Exercise 8 Page 868

We are given results of a poll organized in a matrix. & cc For & Against c Proposition1 Proposition2 Proposition3 & [ cc 1553 & 771 689 & 1633 2088&229 ] In this case, we can treat the matrix as a two-way frequency table. In order to select the conclusion that is not valid, let's check the given conclusions one by one.

Option F

This conclusion states that there were 771 votes cast against Proposition 1. Let's take a look at the results and highlight the number of votes against Proposition 1. & cc For & Against c Proposition1 Proposition2 Proposition3 & [ cc 1553 & 771 689 & 1633 2088&229 ] We can see that 771 votes were cast against Proposition 1, which means that the given statement is correct. Therefore this conclusion is valid.

Option G

Here we will check if more people voted against Proposition 1 than voted for Proposition 2. We have already verified that 771 people voted against Proposition 1. Let's highlight the number of votes for Proposition 2. & cc For & Against c Proposition1 Proposition2 Proposition3 & [ cc 1553 & 771 689 & 1633 2088&229 ] There were 689 people for Proposition 2. This is less than 771. ccc Votes Against & & Votes For Proposition1 && Proposition2 771 & > & 689 This means that our conclusion is valid.

Option H

Proposition 2 has little chance of passing if many more votes were cast against it than for it. We have already found that 689 people voted for Proposition 2. Let's highlight the number of votes against Proposition 2. & cc For & Against c Proposition1 Proposition 2 Proposition3 & [ cc 1553 & 771 689 & 1633 2088&229 ] There were 689 people who voted for the proposition, while there were 1633 people who voted against it. Because 1633 is much bigger than 689, the proposition has little chance of passing. Therefore, the conlusion is valid.

Option J

This conclusion says that more people voted for Proposition 1 than for Proposition 3. We will highlight the number of votes for each proposition. & cc For & Against c Proposition1 Proposition2 Proposition3 & [ cc 1553 & 771 689 & 1633 2088 & 229 ] We can see that 2088 people voted for Proposition 3, which is more than the 1553 people who voted for Proposition 1. ccc Votes For & & Votes For Proposition1 && Proposition3 1553 & < & 2088 This means that this conclusion is not valid. Therefore, the correct answer is option J.