|
STAtistics / Mr. Hansen |
Name: _______________________ |
General Instructions: Raise your hand if you have a question. Write answers in the space provided. If you need additional room, write “OVER” and use reverse side.
Part I: Notation (20 points).
Write the symbol or
standard abbreviation for each term.
1. Sample mean = _______________
2. Population standard deviation =
_______________
3. 
= _______________
4. The 75th percentile =
_______________
5. Graph showing normality as a
straight pattern, skewness as a bent pattern = ________
6. An indicator of both strength and direction of linear correlation = _______________
Part II: Short Answer (2 pts./blank, 20 pts. total).
Fill in each blank with the word,
symbol, or phrase that best fits.
7. For males, greater height is associated with reduced comfort
in airplane seats. If both quantities are expressed as quantitative variables,
we would say that height and comfort level are _____________________
associated.
8. In mathematics, the term parameter
means an “adjustable constant” or a value that determines the shape of a
relationship between quantities. In statistics, the term parameter means __________________________________________ .
9. The two parameters of a normal distribution, in the mathematical
sense, are ______________ , which measures central tendency, and ______________
, which measures dispersion. In other words, these two values together will
determine the position and width of the curve. Do these two quantities also
serve as parameters in the statistical sense of the word? ______________
10. In a linear regression, the value _____ , known as the coefficient of determination, tells us what part (as a decimal fraction) of the variation in the response variable can be explained by variation in the ______________ variable.
11. If r = –.847, we would say that there is a ___________ ___________ ___________ association between the variables in our scatterplot.
Part III. Essay (10
pts.).
If r = .0015, can we conclude that there are no patterns in our data? Try to mention at least two types of patterns that could be present even though the r value is so low. Complete sentences are not required, and you may be very concise, especially if you use visual aids.
Part IV. Regression Exercise (24 pts.).
Show adequate work and circle your answers. For scatterplots, be sure to
show units and the name of the variable on each axis.
Mr. Hansen’s geometry students (n = 15) were asked to guess Mr. Hansen’s age and the headmaster’s age. Results are shown in the table.
|
Guess (Mr. Hansen) |
Guess (Mr. Wilson) |
|
37 |
62 |
|
38 |
62 |
|
42 |
62 |
|
44 |
64 |
|
45 |
67 |
|
40 |
58 |
|
39 |
62 |
|
38 |
57 |
|
40 |
63 |
|
41 |
61 |
|
46 |
65 |
|
46 |
66 |
|
42 |
62 |
|
40 |
59 |
|
57 |
77 |
13. Make a scatterplot with LSRL overlaid.
14. Give the LSRL equation and define all variables used.
15. Is the relationship roughly linear? Give evidence in support of your
answer.
16. Describe the nature of the relationship (in terms of guessing propensities)
without using any math or stat terms.
17. Circle the outlier on your scatterplot. Should it be discarded? _____ Why
or why not?
18. State the slope: _______________
19. Interpret the slope in context.
20. Predict the age that a student would guess Mr. Wilson to be if the student
thought Mr. Hansen was 43. Show your work.
Part V. Normal
Probabilities (26 pts.).
Do not show calculator notation.
Points will be deducted if you show calculator notation, just as on the AP.
Instead, show rough sketches of normal curves and shaded areas.
For problems 21-23, assume that Ms. Denizé has administered
a test having 
= 71, s = 10.5. Assume that the distribution
of scores is approximately normal.
21. Find the 50th, 75th, and 90th percentiles. Show sketches of your normal curves.
22. Find the normalized scores
corresponding to test scores of 68, 71, and 94. Show sketches of your normal curves or some other suitable work.
23. Approximately what percentage of students scored below 65? below 71?
between 69 and 79? Show sketches of your
normal curves.