AP Statistics / Mr. Hansen
4/27/2001

Name: _________________________

Instructions: Circle the letter of the best choice. If no item is completely correct, select the one that is closest. Multiple-choice scoring is +3 points for each correct answer, –¾ point for each incorrect answer, and 0 points for each omission. To speed the grading, please write "omit" if you are omitting a question. There are also two brief free-response questions (#7 and #11) that are worth 3 points each. If you get everything perfectly correct, you will earn 33 points out of 30.

Description of problem: In one of my classes, not STAtistics, I measured the following data for 18 students in the first quarter and first semester. My objectives are (1) to see whether the first quarter average can be used as a good predictor of first semester performance, (2) the strength and direction of the linear association, and (3) the significance, if any, of that association.

Important: After you enter the data in your calculator, use 2-Var Stats to make sure that the mean of the first quarter scores is 86.18888889 and that the mean of the first semester scores is 86.73888889. If you get anything else, you have made a data entry error and should correct it before proceeding. (Otherwise, you will probably get all the answers wrong.)

First quarter avg.

First
semester
avg.

89.2

91.4

84.6

85.2

78.4

74.9

81.6

79.5

90.7

90.2

95.3

98.8

66.8

70.3

69.6

74.6

103.7

98.4

(continued on next page)

96.1

93.6

83.4

81.0

79.6

84.6

99.0

102.3

82.9

80.9

83.1

86.4

85.9

87.7

81.9

82.3

99.6

99.2

0.

Write your initials here ___________ if you obtained the correct values for the sample means of column 1 and column 2.

1.

The linear correlation coefficient when first semester average is regressed on first quarter average is approximately . . .
(A) .9114
(B) .9214
(C) .9314
(D) .9414
(E) .9514

2.

The linear correlation coefficient when first semester average is treated as the explanatory variable and first quarter average as the response variable is . . .
(A) same as the answer to #1
(B) reciprocal of the answer to #1
(C) negative of the answer to #1
(D) negative reciprocal of the answer to #1
(E) none of the above

3.

The percentage of variation in first semester average that can be explained by variation in first quarter average is approximately . . .
(A) 91%
(B) 92%
(C) 93%
(D) 94%
(E) 95%

4.

The slope of the least-squares regression line relating first quarter average (explanatory) to first semester average (response) is approximately . . .
(A) –.794
(B) –.887
(C) .794
(D) .887
(E) 10.329

5.

The standard error of the slope of the least-squares regression line described in #4 is approximately . . .
(A) .0717
(B) .0814
(C) 1.389
(D) 2.946
(E) 10.329

6.

Is the t test for linear regression slope valid in this case?
(A) Yes.
(B) No, because the residual plot shows evidence of nonlinearity.
(C) No, because the residual plot shows evidence that the standard error about the line is larger for extreme values of the explanatory variable.
(D) No, because there is a strong indication of nonnormality in the explanatory variable.
(E) No, because there is a strong indication of nonnormality in the residuals.

7.

In the space below, sketch the plot(s) that you need to check as part of the process of verifying assumptions for the linear regression t test. Rough sketching is perfectly acceptable, but please label the axes.

8.

What can you say about the choices in problem #6, concerning techniques for deciding whether the model satisfies assumptions for the t test for linear regression slope?
(A) In #6, choices B through E all describe things we would need to check.
(B) Choice B in #6 is something we would never check.
(C) Choice C in #6 is something we would never check.
(D) Choice D in #6 is something we would never check.
(E) Choice E in #6 is something we would never check.

9.

On the AP exam, which of the following is not really an acceptable method of checking for normality? (In other words, choose the one that does not give sufficient information to support or refute a rough claim of normality.)
(A) normal quantile plot (a.k.a. normal probability plot)
(B) boxplot
(C) stemplot
(D) histogram
(E) Any one of the above would be a perfectly acceptable method of checking for normality.

10.

If a student scores 78.3 as his first quarter average, what does the model predict will be his first semester average?
(A) 79.1
(B) 79.3
(C) 79.5
(D) 79.7
(E) 79.9

11.

Write your hypotheses and conclusion for a linear regression t test designed to assess whether there is a positive correlation between first quarter average and first semester average. Do not show your work.