## Related questions with answers

Use the following data:

$\begin{matrix} x_i& \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ y_i & \text{3} & \text{7} & \text{5} & \text{11} & \text{14}\\ \end{matrix}$

Use the $t$ test to test the following hypotheses $( \alpha = .05 ) :$

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

$H _ { \mathrm { a } } : \beta _ { 1 } \neq 0$

Solutions

VerifiedThe $t$ statistic for this test is given by the formula:

$t=\dfrac{b_1}{s_{b_1}}.$

Results previous part of this previous exercise:

$\begin{aligned} n&=\text{Sample size}=5 \\ b_1&=\text{Slope}=2.6 \\ s_{b_1}&=\text{Standard error of the slope}=0.6429 \\ \alpha&=\text{Significance level}=0.05 \end{aligned}$

In this exercise, we execute a hypothesis test to check for a significant linear relationship.

*How do you execute a hypothesis test?*

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