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Question
Math
Posted 2 months ago

Kadence took a random sample of 24 students at her school and asked them how much they typically slept on a school night versus a weekend night. Here is computer output from a least-squares regression analysis on her sample:

Regression: weekend vs. school night
\begin{tabular}{lrr} 
Predictor & Coef & SE Coef \\
\hline Constant & 3.182 & 2.319 \\
School night & 0.789 & 0.237 \\
S =1.75=1.75 & R-sq =20.9%=20.9 \% &
\end{tabular}

Assume that all conditions for inference have been met.
Which of these is an appropriate test statistic for testing the null hypothesis that the population slope in this setting is 0 ?

Choose 1 answer:
(A) t=0.7890.237t=\frac{0.789}{0.237}
(B) t=0.7891.75t=\frac{0.789}{1.75}
(C) t=0.7890.209t=\frac{0.789}{0.209}
(D) t=3.1822.319t=\frac{3.182}{2.319}
(E) t=3.1821.75t=\frac{3.182}{1.75}
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 2
The estimate of the slope is given as 0.789 and the standard error of the slope is 0.237
step 3
We calculate the test statistic using the values from step 2: t=0.7890.237t = \frac{0.789}{0.237}
step 4
Using the asksia-ll calculator result, the calculation is t=0.7890.237=3.3291139240506329113924050632911392405063291139240506329113924050...t = \frac{0.789}{0.237} = 3.3291139240506329113924050632911392405063291139240506329113924050...
step 5
The test statistic is approximately t=3.33t = 3.33
A
Key Concept
Test Statistic for Slope in Regression
Explanation
The test statistic for the slope in a regression analysis is found by dividing the estimated slope coefficient by its standard error.

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