Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

Complete the following questions to practice the skills you have learned in this lesson.

1. The number of hours worked, $x$ , and the total dollars earned, $y$ , have a strong positive relationship.

Explain what it means to have a strong positive relationship in this situation.

As the number of hours worked increases, the total dollars earned remains unchanged.
As the number of hours worked decreases, the total dollars earned increases.
As the number of hours worked increases, the total dollars earned increases.
As the number of hours worked increases, the total dollars earned decreases.

2. The number of minutes on the phone and the customer satisfaction rating have a weak negative relationship.

Explain what it means to have a weak negative relationship in this context.

As the number of minutes the customer waits on the phone increases, the customer satisfaction rating increases.
As the number of minutes the customer waits on the phone decreases, the customer satisfaction rating decreases.
As the number of minutes the customer waits on the phone decreases, the customer satisfaction rating remains unchanged.
As the number of minutes the customer waits on the phone increases, the customer satisfaction rating decreases.

For questions 3 to 6, use a graphing calculator to answer the questions. Technology required.

Use technology to find the equation of the line of best fit. What is the value of the correlation coefficient?

x	y
5	2
6	4.6
7.5	7.2
8	8.4
8.3	8.2
9	9.1
10.2	10.3
11.4	9.9
11.4	11
12	12.5

Table 3.5.0

$r \approx -0.04$
$r \approx 0.04$
$r \approx 0.96$
$r \approx -0.96$

For questions 4–6, use the following scenario.

The Collegiate Review publishes information about colleges and universities. The data below are for six public 4-year colleges in New York. Graduation rate is the percentage of students who graduate within six years. Student-to-faculty ratio is the number of students per full-time faculty member.

School	Number of Full-Time Students	Student-to-Faculty Ratio	Graduation Rate
CUNY Bernard M. Baruch College	11,477	17	63
CUNY Brooklyn College	9,876	15.3	48
CUNY City College	10,047	13.1	40
SUNY at Albany	14,013	19.5	64
SUNY at Binghamton	13,031	20	77
SUNY College at Buffalo	9,398	14.1	47

4. Use technology to calculate the value of the correlation coefficient between the number of full-time students and graduation rate. Let

x

represent the number of full-time students and

y

represent the graduation rate. Round to the nearest hundredth.

$𝑟≈0.27$
$𝑟≈−0.83$
$𝑟≈0.83$
$𝑟≈−0.27$

5. Is the linear relationship between graduation rate and number of full-time students weak, moderate, or strong?

strong
moderate
weak

6. Let

x

represent the student-to-faculty ratio and the

y

represent the graduation rate. Use technology to calculate the value of the correlation coefficient between the student-to-faculty ratio and the graduation rate. Round to the nearest hundredth.

$r \approx -0.05$
$r \approx 0.05$
$r \approx -0.95$
$r \approx 0.95$

3.5.5 Practice