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 $=1.75$ & 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) $t=\frac{3.182}{1.75}$
```

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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: $t = \frac{0.789}{0.237}$

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.

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