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Topic: WS/Test Unit 2
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Al Coons

Posts: 898
Registered: 12/4/04
WS/Test Unit 2
Posted: Oct 18, 1996 5:25 PM
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Below is my test on Unit 2 of Workshop Statistics (plus supplemental reading
in BPS). It is not as conceptual as I would have liked although the
students felt it was a fair test. Suggestions for changes? alternate
conceptual questions?

No need to ask permission to use this material (just let me know how it went,
what you think, other problems you gave, other tests you gave)

Thanks,

Al

-----------------------------
10/17/96 AP Statistics - Test 2 - Unit 2 - Topics 6-10 Mr. Coons

1. All but one of the following statements contain a blunder. Which statement
is that? VERY BRIEFLY explain the blunder in the others. (Adopted from
BPS/Moore)

a. There is a correlation of 0.54 between the position a football player
plays and their weight.

b. The correlation between planting rate and yield of corn was found to be r
= 0.23.

c. The correlation between the height and weight of teenage males is r = 0.71
INCHES/POUND.

d. We found the weight & fuel consumption of automobiles to be highly
correlated (r = -1.09).

2. Briefly but clearly discuss the danger of extrapolating. A clear sketch
can accompany your written explanation.

3. DO NOT ENTER THIS DATA INTO YOUR CALCULATOR.(Adopted from Rossman's Exams)


In a study of whether a relationship exists between a child's aptitude and
the age at which he/she first speaks, researchers recorded the age (in
months) of a child's first speech and the child's score on an aptitude test.
These data for these 21 children follow:

child 1 2 3 4 5 6 7 8 9 10 11
age 15 26 10 9 15 20 18 11 8 20 7
score 95 71 83 91 102 87 93 100 104 94 113

child 12 13 14 15 16 17 18 19 20 21
age 9 10 11 11 10 12 42 17 11 10
score 96 83 84 102 100 105 57 121 86 100

The least squares line for predicting aptitude score from age at first
speech turns out to be:

aptitude score = 110 - 1.13 * age

The value of the correlation coefficient is -0.640. x-mean is approximately
14. y-mean is approximately 94.

The scatterplot below displays this relationship.

[SCATTERPLOT]

a. To one decimal place, what would the least squares line predict for the
aptitude score of a child who first spoke at 20 months?

b. Calculate the residual for child number 6. Show your work.

c. Judging from the scatterplot, which child has the largest (in absolute
value) residual? What is unusual about this child?

d. Which child has the smallest fitted value?

e. Which child seems to be the most influential observation?

f. Without entering the data into your calculator, determine The Coefficient
of Determination. In one sentence describe what this value tells us for this
data set?
g. On your answer sheet, draw and fully annotate (label) all values and
descriptions relating to the data for child #19 which illustrate your
understanding of The Coefficient of Determination (r^2)

4. Note: The data for this problem is stored in a program named SURFACE
which is available from Mr. Coons.

The following data give weight (kg) and surface area (meters2) of human
beings who are the same height.

Weight 70 75 77 80 82 84 87 90 95 98
Surface Area 2.01 2.12 2.15 2.2 2.22 2.3 2.3 2.3 2.33 2.3

a. Using weight as the independent variable, state the value of and
interpret the slope of the regression line.

b. State the value of and interpret the y-intercept of the regression line.

c. Draw very quick sketch of the residual plot for this model.

d. On the right is the residual plot of a quadratic fit to the above data.
Which of the two models is most appropriate. Why?

[RESIDUAL PLOT]


5. a) State, without example, Simpson's Paradox.

b) Create a numerical example of Simpson's Paradox. Briefly explain how the
example demonstrates this deceiving situation.

6. Your AP STATS formula sheet has the following three formulas which relate
to linear regression.

y = ax + b, b = r *s(y)/s(x), a = y-mean - b(x-mean)

Show that the regression line always contains the point (x-mean, y-mean)


A little extra credit - all or nothing

If you were a teacher, how would you explain that the result in the last
problem makes sense conceptually?








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