Exercise 5 Page 694

We know that there are $100$ students that do not have an after-school job. Out of these $100$ students, $67$ students are on the honor roll. Let's create a two-way frequency table.

	Have an After-School Job	Do Not Have an After-School Job	Total
On the Honor Roll		$67$
Not on the Honor Roll
Total		$100$

Now let's look at Jasmine's interpretation of the data!

We want to find Jasmine's mistake. To do so, we will calculate the relative frequencies by row. We can find the frequency by calculating the ratio of the number of the students that are on the honor and do not have an after-school jobs to the total number of students on the honor roll. Notice that we do not know the total number of students on the honor roll. This means that the statement made by Jasmine is incorrect.

Next, we also know that there are $100$ students who do not have a job. This means that we can calculate the conditional relative frequency by column. To do so, we will calculate the ratio of the number of the students that are on the honor roll and do not have after-school jobs to the total number of students who have an after-school job.

	Have an After-School Job	Do Not Have an After-School Job	Total
On the Honor Roll	$?$	$67;\frac{67}{100}=0.67$	$?$
Not on the Honor Roll
Total		$100$

Looking at the table, we can see that the relative frequency of students that do not have an after-school job and are on the honor roll to the total number of students who do not have a job is $0.67.$ This means that Jasmine should have said that more than half of the students that do not have after-school jobs are on the honor roll.