Homework Problems due 2/5:



1. A set of 15 exam scores is as follows:
75, 84, 68, 95, 87, 93, 56, 87, 83, 82, 80, 62, 91, 84, 75
a. Draw a dotplot of the scores.
b. Draw a stem-and-leaf plot of the scores.
c. Make a five number summary.
d. Using part c., draw a boxplot.

2. You are looking at a computer printout of 100 test scores, which have been converted to standard units. The first 10 entries are
-6.2, 3.5, 1.2, -0.13, 4.3, -5.1, -7.2, -11.3, 1.8, 6.3
Does the printout look reasonable, or is something wrong with the computer?

3. Which of the following are true? false? Explain or give examples.
a. The median and the average of any list are always close together.
b. Half of a list is always below average.
c. With a large, representative sample, the histogram is bound to follow the normal curve quite closely.
d. If two lists of numbers have exactly the same average of 50 and the same SD of 10, then the percentage of entries between 40 and 60 must be exactly the same for both lists.

4. Find the areas under the standard normal curve. (You can try this now. We will do more examples on Monday if you want to wait.)
a. Between z=-1.75 and z=2.05.
b. Between z=-3.35 and z=-1.10.
c. Above z=-2.00.

5. The following list of test scores has an average of 50 and an SD of 10:
39, 41, 47, 58, 65, 37, 37, 49, 56, 59, 62, 36, 48
52, 64, 29, 44, 47, 49, 52, 53, 54, 72, 50, 50
a. Use the normal approximation to estimate the number of scores within 1.25 SDs of the average.
b. How many scores really were within 1.25 SDs of the average?

6. In its Fuel Economy Guide for 2008 model vehicles, the Environmental Protection Agency gives data on 1152 vehicles. There are a number of outliers, mainly vehicles with very poor gas mileage. If we ignore the outliers, however, the combined city and highway gas mileage of the other 1120 or so vehicles is approximately Normal with mean 18.7 miles per gallon (mpg) and standard deviation 4.3 mpg.
a. The 2008 Chevrolet Malibu with four-cylinder engine has combined gas mileage 25 mpg. What percentage of all vehicles have worse gas mileage than the Malibu?
b. How much must a 2008 vehicle's gas mileage be in order to fall in the top 10% of all vehicles?
(The distribution omits a few high outliers, mainly hybrid gas-electric vehicles.)

7. Heights for college women are normally distributed with mean = 65 inches and standard deviation = 2.7 inches.
a. Find the height such that about 25% of college women are shorter than that height. What is the percentile ranking for that height?
b. Find the height such that about 15% of college women are taller than that height. What is the percentile ranking for that height?

8. For each of the following pairs of variables, is there likely to be a positive association, a negative association, or no association? Briefly explain your reasoning.
a. Amount of alcohol consumed and performance on a test of coordination.
b. Height and grade point average for college students.
c. Miles of running per week and time for a 5-kilometer run.
d. Forearm length and foot length.

9. The figure for this exercise is a scatterplot of y = average math SAT score in 1998 versus x = percent of graduating seniors who took the test that year for the 50 states and the District of Columbia.

a. Does the plot show a positive association, a negative association, or no association between the two variables? Explain.
b. About what was the highest average math SAT for the 50 states and District of Columbia? Approximately, what percent of graduates took the test in that state?
c. About what was the lowest average math SAT for the 50 states and District of Columbia? Approximately what percent of graduates took the test in that state?

10. The following table shows the relationship between the speed of a car (mph) and the average stopping distance (feet) after the brakes are applied:
Speed (mph) 0 10 20 30 40 50 60 70
Distance (ft) 0 20 50 95 150 220 300 400
a. In the relationship between these two variables, which is the response variable (y) and which is the explanatory variable (x)?
b. Draw a scatterplot of the data. Characterize the relationship between stopping distance and speed.

11. A study of the IQs of husbands and wives obtained the following results:
for husbands,   average IQ = 100,   SD = 15
for wives,        average IQ = 100,   SD = 15
                                          r = 0.6
One of the following is a scatter diagram for the data. Which one? Say briefly why you reject the others.


12. Suppose men always married women who were exactly 8% shorter. What would the correlation between their heights be?

13. The figure below has six scatter diagrams for hypothetical data. The correlation coefficients, in scrambled ordered, are:
-0.85    -0.35    -1.00    0.06    0.97    0.62
Match the scatter diagrams with the correlation coefficients.


14. Find the correlation coefficient for each of the three data sets shown below.

(a)
xy
15
13
15
17
23
23
21
31
31
41

(b)
xy
11
12
11
13
21
24
21
32
32
43

(c)
xy
12
12
12
12
24
24
24
36
36
48


15. In a large psychology study, each subject took two IQ tests (form L and form M of the Stanford-Binet). A scatter diagram for the test scores is sketched below. You are trying to predict the score on form M from the score on form L. Each prediction is off by some amount. On the whole, will these prediction errors be smaller when the score on form L is 75, or l25? or is it about the same for both?


16. A teaching assistant gives a quiz with 10 questions and no part credit. After grading the papers, the TA writes down for each student the number of questions the student got right and the number wrong. The average number of right answers is 6.4 with an SD of 2.0; the average number of wrong answers is 3.6 with the same SD of 2.0. The correlation between the number of right answers and the number of wrongs is
0    -0.50    +0.50    -1    +1    can't tell without the data
Explain.

17. Start thinking about your Project Proposal, due Friday, 2/19.



Reading:

"The Median Isn't the Message", by Stephen Jay Gould, Discover, June 1985. The article is available online at the Cancer Guide website. If that doesn't work, we have a link to a local copy.

Possible Essay Questions: