Use the following data set for Exercises 10–13.

18.7 2 100 4.1
18.4 4 90 5.0
21.8 6 90 3.8
22.0 8 70 5.2
25.2 10 70 3.8
25.7 12 50 5.3
26.9 14 50 5.4
28.3 16 30 5.4
28.6 18 30 4.3
31.8 20 10 4.9

Question 13.155

11. Perform the test for the significance of the individual predictor variables, using level of significance . Do the following:

  1. For each hypothesis test, state the hypotheses and the rejection rule.
  2. For each hypothesis test, find the statistic and the -value.
  3. For each hypothesis test, state the conclusion and interpretation.

13.99.11

(a) Test : There is no linear relationship between and . : There is a linear relationship between and . Reject if the -value . Test : There is no linear relationship between and . : There is a linear relationship between and . Reject if the -value . Test : There is no linear relationship between and . : There is a linear relationship between and . Reject if the -value . (b) Test , with ; Test , with ; Test 3: , with . (c) Test 1: The , which is not . Therefore we do not reject . There is insufficient evidence of a linear relationship between and . Test 2: The , which is not . Therefore we do not reject . There is insufficient evidence of a linear relationship between and . Test 3: The , which is not . Therefore we do not reject . There is insufficient evidence of a linear relationship between and .