Question

Math

Posted 3 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) $t=\frac{0.789}{0.209}$
() $t=\frac{3.182}{2.319}$
(E) $t=\frac{3.182}{1.75}$
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

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.

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