CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 15. Concepts of Statistics

In general, at this point you should use your best judgment when choosing a function family to model a given set of
data and deciding how good a fit the model is based on context.
Example A
Given the following data about SAT scores and number of hours slept the night before, use an appropriate function
family to produce a reasonable model. Defend your choice of function families.

TABLE15.16:

# Hours Slept SAT Score

8.5 1840

10.9 1510

9.1 1900

7.5 2070

7.2 1550

6.0 1720

2.3 840

5.5 1230

Solution:Letxbe the number of hours slept andybe the SAT score.
After plotting the points, you should choose a function family to use as a model. In this case, it would be appropriate
to try a quadratic relationship.

A quadratic model makes sense because there seems to be a peak in the model and in the data around 8.5 hours of
sleep. It makes sense that someone who does not get enough sleep will do worse and someone who gets too much
sleep might also do worse.
Example B
Using the model from Example A, answer the following questions.

a. What is the perfect amount of sleep to get before the SATs?

b. Calculate the score you are predicted to get if you get 5 hours of sleep.

c. What is the relevant domain of the model?

d. The average SAT score is about 1500. According to the model, what amount of sleep predicts this score? Does

this number represent the average number of hours that people sleep before the SATs?

e. Compare the actual and predicted score for someone with 6 hours of sleep.

Solution: