The SAT and ACT are the two major standardized tests that colleges use to evaluate applicants. Most students take just one of these tests. However, some students take both. This Excel file gives the scores of 60 students who took both tests. Can we relate the two tests? Plot the data with SAT on the x axis and ACT on the y axis and answer the questions below.
Student SAT ACT
1 1000 24
2 870 21
3 1090 25
4 800 21
5 1010 24
6 880 21
7 860 19
8 1040 24
9 920 17
10 850 22
11 740 16
12 840 17
13 840 19
14 780 22
15 500 10
16 1060 25
17 830 19
18 830 20
19 780 12
20 870 21
21 1440 32
22 1190 30
23 1120 27
24 1120 25
25 490 7
26 800 16
27 590 12
28 800 18
29 1050 23
30 830 16
31 990 24
32 960 27
33 870 18
34 890 23
35 700 16
36 880 21
37 970 21
38 880 24
39 930 22
40 1020 24
41 920 22
42 980 27
43 860 23
44 790 14
45 810 19
46 1030 23
47 420 21
48 620 18
49 1080 23
50 1220 30
51 800 20
52 1150 28
52 1000 19
54 1080 22
55 1140 24
56 970 20
57 1030 25
58 970 20
59 920 21
60 1060 24
Question 1. Find the slope and intercept of the least squares regression line (draw the least squares line on your plot).
intercept (use 4 decimal places)
1.6263
slope (use 4 decimal places)
.0214
Question 2. Give the value of the test statistic for a test of H0: ß1 = 0.
(use 4 decimal places)
Question 3. If the alternative hypothesis is Ha: ß1 ? 0, what is the rejection region if the significance level of the test is a = .05? Use this t-table to determine your answer.
t =
t =
Question 4. What is the correct conclusion for this hypothesis test?
Do not reject the null hypothesis H0; the SAT score is not useful for predicting the ACT score.
Reject the null hypothesis H0 and conclude that in a linear model SAT score is useful for predicting the ACT score.
Question 5. Determine a 95% confidence interval for the slope ß1 of the least squares line (use 3 decimal places in your answers; use this t-table to determine the correct t-value).
lower endpoint of confidence interval
upper endpoint of confidence interval