Use the following information for questions:
A representative sample of n = 12 male college students is used to find a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation is $\hat{y}$ = 30 + 2 x. The standard error of the estimated slope is 1. The following hypotheses will be tested:
H 0 : $β_1 = 0$
H a :$β_1 ≠ 0$
-What is the p-value for the test? (Table A.3 or its equivalent needed.)
A) 0.074
B) 0.162
C) 0.226
D) None of the above

Question

Use the following information for questions:
 A representative sample of n = 12 male college students is used to find a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation is $\hat{y}$ = 30 + 2 x. The standard error of the estimated slope is 1. The following hypotheses will be tested:
H 0 : $β_1 = 0$
H a :$β_1 ≠ 0$
-What is the p-value for the test? (Table A.3 or its equivalent needed.)
A) 0.074
B) 0.162
C) 0.226
D) None of the above

Quizplus · Accepted Answer

The test statistic for the slope is calculated as $ t = \frac{b_1 - 0}{SE(b_1)} = \frac{2 - 0}{1} = 2 $. With n - 2 = 10 degrees of freedom, the p-value for a two-tailed test with t = 2 is approximately 0.074.

Use the Following Information for Questions: a Representative Sample y^\hat{y}y^​

Use the Following Information for Questions:
a Representative Sample $\hat{y}$