Use the following information for questions:
Data from a sample of 10 student is used to find a regression equation relating y = score on a 100-point exam to x = score on a 10-point quiz. The least squares regression equation is $\hat{y}$ = 35 + 6 x. The standard error of the slope is 2. The following hypotheses are tested:
H₀: $β_1=0$
H_a: $β_1≠0$
-What is a 95% confidence interval for $\beta$ ₁ ? (Table A.2 or its equivalent needed.)

Question

Use the following information for questions:
Data from a sample of 10 student is used to find a regression equation relating y = score on a 100-point exam to x = score on a 10-point quiz. The least squares regression equation is

\hat{y}

= 35 + 6 x. The standard error of the slope is 2. The following hypotheses are tested:
H₀:

β_1=0

H_a:

β_1≠0

-What is a 95% confidence interval for

\beta

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

Quizplus · Accepted Answer

The 95% confidence interval for the slope $β_1$ is calculated using the formula: $\hat{β}_1 \pm t_{\alpha/2, n-2} \times SE(\hat{β}_1)$, where $\hat{β}_1 = 6$, $SE(\hat{β}_1) = 2$, and $n = 10$. For a 95% confidence level and 8 degrees of freedom (n-2), the t-value from Table A.2 (or equivalent) is approximately 2.306. Thus, the confidence interval is $6 \pm 2.306 \times 2$, which calculates to (1.388, 10.612), rounded to (1.38, 10.62).

Use the Following Information for Questions: Data from a Sample

Use the Following Information for Questions:
Data from a Sample