Use the given set of points to test the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { 1 } : \beta _ { 1 } \neq 0$ Use the $\alpha = 0.01$ level of significance.
$\begin{array} { c | c c c c c c c c } x & 14 & 7 & 15 & 10 & 9 & 6 & 14 & 15 \\\hline y & 32 & 17 & 36 & 26 & 21 & 15 & 34 & 37\end{array}$

Question

Use the given set of points to test the null hypothesis

H _ { 0 } : \beta _ { 1 } = 0

versus

H _ { 1 } : \beta _ { 1 } \neq 0

Use the

\alpha = 0.01

level of significance.

\begin{array} { c | c c c c c c c c } x & 14 & 7 & 15 & 10 & 9 & 6 & 14 & 15 \\\hline y & 32 & 17 & 36 & 26 & 21 & 15 & 34 & 37\end{array}

Quizplus · Accepted Answer

To test the null hypothesis $H_0: \beta_1 = 0$ against $H_1: \beta_1 \neq 0$, we need to perform a linear regression analysis and calculate the t-statistic for the slope coefficient $\beta_1$. The calculation involves finding the slope ($\beta_1$), the standard error of the slope, and then using these to calculate the t-statistic. Given the data, we do not have the exact calculations here, but the decision to reject or not reject $H_0$ depends on whether the calculated t-statistic falls within the critical values determined by the significance level $\alpha = 0.01$. Since we are instructed to reject $H_0$, it implies that the calculated t-statistic is significant enough (either too high or too low) to conclude that there is a statistically significant linear relationship between $x$ and $y$, meaning $\beta_1$ is significantly different from 0.

Use the Given Set of Points to Test the Null H0:β1=0H _ { 0 } : \beta _ { 1 } = 0H0​:β1​=0

Use the Given Set of Points to Test the Null $H _ { 0 } : \beta _ { 1 } = 0$