Test #1, 10/1/1998

General Instructions: Raise your hand if you have a question. Write answers in the space provided. Use additional notebook paper or graph paper of your own if you need additional room.

Fill in the official name and standard notation for each of the following. The first one has been done for you as an example.

All of the numbered statements below are false. In each case, make a minor change (such as adding a word or two, crossing a few words out, or changing the wording) to make the statement true. However, you may not simply add or subtract the word "not" (since, obviously, that would be too easy). The first one has been done for you as an example. Important: Make changes that demonstrate your knowledge of the subject matter. Points will be deducted if you take the easy way out (for example, changing "useful" to "fairly useless" in #12).

[to make correction, cross out 2.5 IQR and write 1.5 IQR]
7. Although human judgment is better, the "2.5 IQR" ^ rule is useful in cases where automated determination of outliers is needed.

AP Statistics / Mr. Hansen

Test #1, 10/1/1998 (continued)

Use your knowledge of statistical methods to solve the following problems. Your graphing calculator will probably be a big help to you on most of these.

Judge Jake Jones (known as the Law of Speed Trap, South Carolina) is known far and wide for the strictness of his speeding fines. The speed limit within the town of Speed Trap is 55 mph. Interstate 55 (get it?) passes through his jurisdiction and has been generating a reliable source of revenue for many years. Recently a researcher studied the speed of people ticketed on this stretch of I-55 and the fine that Judge Jake assessed in each case. A representative subset of the data (shown below) might make a tempting regression study.

Fine assessed	Speed (according to radar)
$190	72 mph
$170	77 mph
$145	65 mph
$175	69 mph
$175	70 mph
$150	65 mph
$135	62 mph
$170	71 mph

13. First, code the speeds as speeds in excess of the speed limit, and create a stemplot with "stems" at 0, 5, 10, etc. Show your stemplot. What conclusions, if any, can you draw about the distribution of speeds from this stemplot? Provide at least one sentence of explanation.

14. Compute the five-number summary for the coded speed data. No need to show work.

15. Compute the standard deviation of the coded speed data. No need to show work.

16. What is the standard deviation of the original speed data (i.e., the values ranging from 62 to 77)? Important: For this problem, you must either show your work (ugh!) or provide a sentence of explanation.

17. Now, let us consider the role of the other column of data (the fines). If we are writing an article for a motorists’ club, we might want to be able to predict the likely fine that would result from various levels of speeding in Judge Jake’s area. What would be the explanatory variable? ______________________ What would be the response variable? _____________________

18. Create a SCATTERPLOT and a suitable regression line that we might be able to use as a way of predicting Judge Jake’s fines. Draw your scatterplot and regression line here.

19. What is the slope of your regression line from #18? ___________________________

20. Is Judge Jake fairly predictable in his assessment of speeding fines? What can you say about the correlation between speed and fine? (Write your answer using AP-style wording.)

21. In our article for the motor club, what would be a reasonable estimate of the fine Judge Jake would slap on a speeder who was clocked doing 70 mph? Show your work.

22. Would it be reasonable to use your regression line to estimate the fine Judge Jake would assess against a speeder clocked at 57 mph? __________ Why or why not? ______________________________________

________________________________________________________

23. The speeder in the sample data who was going 77 mph was given a surprisingly mild fine (surprising, that is, in terms of the regression line). What term do we use when a case has a large deviation from the regression line? ________________________

24. Remove the speeder who was going 77 mph from your data set and recompute the regression line. What is the new slope? _____________________

25. Is the case of the speeder who was going 77 mph an influential observation? ___________ Why or why not? _______________________________________

[The other class had a question about residual plots at this point. Be sure to check the other version of the test for a sample question of this type.]

Questions 26-28 refer to the following scenario. For each question, you must document your assumptions, show a sketch, and write a conclusion. Suppose that the College Board has decided to phase out the SAT and replace it with a new test (the STA?) that has a normal distribution of scores, with a mean of 1500 and a standard deviation of 100.

26. On this new test, what percentage of the test takers will score 1600 or above? Use the shortcut [68-95-99.7 rule] if you know it.

27. Suppose that Joe Bulldog scores 1440 on the new test. What is this in terms of a percentile?

28. What fraction of the students taking the new test will receive scores between 1300 and 1550?

29. Using a digital micrometer, Milton measures the thickness of a sheet of paper. Because he has a scientific attitude, Milton decides to take a number of measurements to (hopefully) reduce the chance of making an error with only one measurement. Here are the results of 11 measurements (in microns): 97, 99, 100, 102, 103, 103, 104, 104, 105, 107, 119. Construct a normal quantile plot and assess the normality of Milton’s measurements. (Note that I have already placed Milton’s measurements in ascending order—a necessary first step. The other thing you need is a column of normal quantiles, which is listed below. If you wish to save some typing, raise your hand and I will link the column NQT to your calculator.) What can you say about the distribution of Milton’s measurements?

-1.691
-1.097
-.7479
-.4728
-.2299
0
.2299
.4728
.7479
1.097
1.691