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 $=1.75$ & R-sq $=20.9 \%$ &
\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) $t=\frac{0.789}{0.237}$
(B) $t=\frac{0.789}{1.75}$
(C) $t=\frac{0.789}{0.209}$
(D) $t=\frac{3.182}{2.319}$
(E) $t=\frac{3.182}{1.75}$

Question

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 $=1.75$ & R-sq $=20.9 \%$ &
\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) $t=\frac{0.789}{0.237}$
(B) $t=\frac{0.789}{1.75}$
(C) $t=\frac{0.789}{0.209}$
(D) $t=\frac{3.182}{2.319}$
(E) $t=\frac{3.182}{1.75}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the appropriate test statistic for testing the null hypothesis that the population slope is 0, we use the formula $t = \frac{ ext{estimate}}{ ext{SE of estimate}}$. ‖ ‖ 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: $t = \frac{0.789}{0.237}$. ‖ ‖ step 4 ⋮ Using the asksia-ll calculator result, the calculation is $t = \frac{0.789}{0.237} = 3.3291139240506329113924050632911392405063291139240506329113924050...$. ‖ ‖ step 5 ⋮ The test statistic is approximately $t = 3.33$. ‖ ***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.⚹◊What is the formula to calculate the test statistic t for testing the null hypothesis that the population slope is 0 in a least-squares regression analysis?⍭ Generate me a similar question◊

Sia