Question

1. a survey found that of 2,000 high school seniors surveyed 1,800 have their driver’s license. of those who have their driver’s license, 1,350 have a job. of the seniors who do not have a driver’s license, 40 have a job.

a. complete the frequency table.

	has a job	does not have a job	total
does not have a driver’s license	40
total			2,000

b. explain how the information in the table or the segmented bar graph can be used to show that there is an association between having a job and having a driver’s license.

Explanation:

Part a: Completing the Frequency Table

Step 1: Find "Does Not Have a Job" for "Has Driver’s License"

We know the total number of students with a driver’s license is 1,800, and 1,350 of them have a job. To find the number of students with a driver’s license who do not have a job, we subtract the number of those with a job from the total with a driver’s license.
\[
1800 - 1350 = 450
\]

Step 2: Find the total number of students without a driver’s license

The total number of high school seniors surveyed is 2,000, and 1,800 have a driver’s license. So the number of students without a driver’s license is:
\[
2000 - 1800 = 200
\]

Step 3: Find "Does Not Have a Job" for "Does Not Have a Driver’s License"

We know 40 students without a driver’s license have a job, and the total number of students without a driver’s license is 200. So the number of students without a driver’s license who do not have a job is:
\[
200 - 40 = 160
\]

Step 4: Find the total number of students with a job

We add the number of students with a job and a driver’s license (1,350) and the number of students with a job and without a driver’s license (40):
\[
1350 + 40 = 1390
\]

Step 5: Find the total number of students without a job

We add the number of students without a job and with a driver’s license (450) and the number of students without a job and without a driver’s license (160):
\[
450 + 160 = 610
\]

Now we can fill in the table:

	Has a Job	Does Not Have a Job	Total
Does Not Have a Driver’s License	40	160	200
Total	1,390	610	2,000

Part b: Explaining the Association

To determine if there is an association between having a job and having a driver’s license, we can compare the conditional probabilities.

• The probability of having a job given that a student has a driver’s license is:

\[
P(\text{Job} | \text{License}) = \frac{1350}{1800} = 0.75
\]

• The probability of having a job given that a student does not have a driver’s license is:

\[
P(\text{Job} | \text{No License}) = \frac{40}{200} = 0.2
\]

Since these two probabilities are not equal (0.75 ≠ 0.2), there is an association between having a job and having a driver’s license. This means that the likelihood of having a job is different for students with a driver’s license compared to those without a driver’s license. A segmented bar graph would visually show these differences in proportions, making it clear that the distribution of having a job is not the same for both groups (with and without a driver’s license).

Answer:

Part a: Completing the Frequency Table

Step 1: Find "Does Not Have a Job" for "Has Driver’s License"

We know the total number of students with a driver’s license is 1,800, and 1,350 of them have a job. To find the number of students with a driver’s license who do not have a job, we subtract the number of those with a job from the total with a driver’s license.
\[
1800 - 1350 = 450
\]

Step 2: Find the total number of students without a driver’s license

The total number of high school seniors surveyed is 2,000, and 1,800 have a driver’s license. So the number of students without a driver’s license is:
\[
2000 - 1800 = 200
\]

Step 3: Find "Does Not Have a Job" for "Does Not Have a Driver’s License"

We know 40 students without a driver’s license have a job, and the total number of students without a driver’s license is 200. So the number of students without a driver’s license who do not have a job is:
\[
200 - 40 = 160
\]

Step 4: Find the total number of students with a job

We add the number of students with a job and a driver’s license (1,350) and the number of students with a job and without a driver’s license (40):
\[
1350 + 40 = 1390
\]

Step 5: Find the total number of students without a job

We add the number of students without a job and with a driver’s license (450) and the number of students without a job and without a driver’s license (160):
\[
450 + 160 = 610
\]

Now we can fill in the table:

	Has a Job	Does Not Have a Job	Total
Does Not Have a Driver’s License	40	160	200
Total	1,390	610	2,000

Part b: Explaining the Association

To determine if there is an association between having a job and having a driver’s license, we can compare the conditional probabilities.

• The probability of having a job given that a student has a driver’s license is:

\[
P(\text{Job} | \text{License}) = \frac{1350}{1800} = 0.75
\]

• The probability of having a job given that a student does not have a driver’s license is:

\[
P(\text{Job} | \text{No License}) = \frac{40}{200} = 0.2
\]

Since these two probabilities are not equal (0.75 ≠ 0.2), there is an association between having a job and having a driver’s license. This means that the likelihood of having a job is different for students with a driver’s license compared to those without a driver’s license. A segmented bar graph would visually show these differences in proportions, making it clear that the distribution of having a job is not the same for both groups (with and without a driver’s license).