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) $t=\frac{0.789}{0.209}$
() $t=\frac{3.182}{2.319}$
(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) $t=\frac{0.789}{0.209}$
() $t=\frac{3.182}{2.319}$
(E) $t=\frac{3.182}{1.75}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To test the null hypothesis that the population slope is 0, we use the t-statistic formula $t = \frac{ ext{estimate} - ext{null value}}{ ext{SE of estimate}}$. ‖ ‖ step 2 ⋮ The estimate of the slope is the coefficient of "School night", which is 0.789. ‖ ‖ step 3 ⋮ The null value of the slope we are testing against is 0. ‖ ‖ step 4 ⋮ The standard error (SE) of the slope estimate is 0.237. ‖ ‖ step 5 ⋮ Plugging the values into the t-statistic formula gives us $t = \frac{0.789 - 0}{0.237}$. ‖ ‖ step 6 ⋮ Calculating the t-statistic, we get $t = \frac{0.789}{0.237}$. ‖ ‖ step 7 ⋮ Using the asksia-ll calculator result, the calculation is $0.789/0.237 = 3.3291139240506329113924050632911392405063291139240506329113924050...$. ‖ ‖ step 8 ⋮ The t-statistic is approximately 3.33. ‖ ∻1 Answer∻ ***A*** ∻Key Concept∻ ⚹t-statistic for hypothesis testing⚹ ∻Explanation∻ ⚹The t-statistic is used to determine if there is a significant difference between the estimated parameter and the null hypothesis value, taking into account the variability of the estimate as measured by its standard error.⚹◊What is the formula for calculating the t-statistic for testing the null hypothesis in linear regression?⍭ Generate me a similar question◊

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