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)
----------------------------- 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:
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.
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.