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:
H₀: $β_1 = 0$
H_a: $β_1 ≠ 0$
-What is a 90% confidence interval for $\beta$ ₁? (Table A.2 or its equivalent needed.)

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:
H₀:

β_1 = 0

H_a:

β_1 ≠ 0

-What is a 90% confidence interval for

\beta

₁? (Table A.2 or its equivalent needed.)

Quizplus · Accepted Answer

The 90% confidence interval for the slope ($β_1$) can be calculated using the formula: $\hat{β}_1 \pm t_{\alpha/2, n-2} \times SE(\hat{β}_1)$, where $\hat{β}_1$ is the estimated slope, $t_{\alpha/2, n-2}$ is the t-value for the desired confidence level and degrees of freedom (n-2), and $SE(\hat{β}_1)$ is the standard error of the slope. Given $\hat{β}_1 = 2$, $SE(\hat{β}_1) = 1$, and for a 90% confidence interval with 10 degrees of freedom (n-12, so n-2=10), the t-value from Table A.2 (or equivalent) is approximately 1.812. Thus, the confidence interval is $2 \pm 1.812 \times 1$, which calculates to (0.188, 3.812), rounded to (0.19, 3.81).

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

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