Elementary Statistics

23. The graph below represents the verbal score and the math score on the 2007 SAT exam for a random sample of 18 Warren High Schools seniors.

(a) This type of graph is called a _______________ (circle your choice) i) dotplot ii) scatterplot iii) boxplot iv) stemplot v) histogram

(b) One of the points on this graph has coordinates (540, 607). Circle this point on the graph.

(c) Write a sentence to explain what the point you circled in part (b) represents in this context.

(d) Complete the sentence by wiring two words that describe the association between the two variables. The association between SAT math and verbal scores is ______________ and _______________.

(e) True or False:

Most students in this sample scored higher on the verbal portion than on the math portion: _____________

24. A statistics students went on line to www.carmax.com and found the price of 5 pre-owned Toyota Camry LE’s and recorded the following information:

Age of Car 7 5 10 2 4 Price of Car $14,599 $13,998 $10,998 $20,599 $15,998

(a) Find the equation of the regression line for predicting the price of the car from the age of the car. Use

the names of the variables in your equation, not x and y.

(b) What is the correlation coefficient? What does it tell you about the linear model? Answer using a

complete sentence. Be specific.

(c) What is the slope the regression line? What does it mean in the context of this problem? Answer using a complete sentence, Be specific.

200

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300 400 500 600 700

SA T

M at

h Sc

or e

SAT Verbal Score

o

0 It represents a Warren High school student who got 540 on the verbal SAT and 607 in the math SAT in 2007 .

strong positive

False

.

Predicted Price = 21158 - 1057 ( Age )

r= - -9188 There is a strong negative correlation between the price of a car and the age of the car .

Slope = - 1057 slope # I¥

On average , the price of a car decreases at a rate of $1,057 per year .

25. A high school math teacher has students maintain records on their daily study time (in minutes) and then compares their average daily study time to the scores received on an exam. The results from a random sample of these students are shown in the graph. The corresponding regression line is

Predicted Exam Score = 58 + 0.6(Study Time)

The correlation coefficient is r = 0.718.

(a) Use the meaning of the slope of the regression line to complete the following sentence:

On average, for each additional 10 minutes of daily study time, students can expect their exam

scores to _________________ by about ___________ points.

(b) What is the y- intercept? Write a sentence to explain what it represent in the context of this problem.

(c) Use your model to predict a student’s exam score if she averages 60 minutes of study time a day.

(d) According to this model, on average, what should a student’s daily study time be if he wants to score 100 points on the test? Show your supporting work clearly.

(e) What percentage of the variability we see in these exam scores can be accounted for by study time?

40 45 50 55 60 65 70 75 80 85 90 95

100

0 20 40 60

Ex am

S co

re

Daily Study Time

slope 0.6 PINI

10 C. 6) = 6

- increase 6

( 0,58 ) → On average , a student that does not study at all can expect an exam score of 58 .

Score = 58+0.6 (60=940

100=58 t . 6× About7OmiT_ 42 = .6×70

= X

÷ . coefficient of determination

F=( 7185=5155 ~~ "

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