Questions: Suppose you computed r=-0.235 using n=42 data points. Using the critical values table below, determine if the value of r is significant or not. df CV (+ and - ) df CV (+ and - ) df CV (+ and - ) df CV (+ and - ) 1 0.997 11 0.555 21 0.413 40 0.304 2 0.950 12 0.532 22 0.404 50 0.273 3 0.878 13 0.514 23 0.396 60 0.250 4 0.811 14 0.497 24 0.388 70 0.232 5 0.754 15 0.482 25 0.381 80 0.217 6 0.707 16 0.468 26 0.374 90 0.205 7 0.666 17 0.456 27 0.367 100 0.195 8 0.632 18 0.444 28 0.361 9 0.602 19 0.433 29 0.355 10 0.576 20 0.423 30 0.349 Select the correct answer below: T is significant because t is between the positive and negative critical values. r is not significant because it is between the positive and negative critical values. ↑ is significant because it is not between the positive and negative critical values r is not significant because it is not between the positive and negative critical values.

Suppose you computed r=-0.235 using n=42 data points. Using the critical values table below, determine if the value of r is significant or not. df CV (+ and - ) df CV (+ and - ) df CV (+ and - ) df CV (+ and - ) 1 0.997 11 0.555 21 0.413 40 0.304 2 0.950 12 0.532 22 0.404 50 0.273 3 0.878 13 0.514 23 0.396 60 0.250 4 0.811 14 0.497 24 0.388 70 0.232 5 0.754 15 0.482 25 0.381 80 0.217 6 0.707 16 0.468 26 0.374 90 0.205 7 0.666 17 0.456 27 0.367 100 0.195 8 0.632 18 0.444 28 0.361 9 0.602 19 0.433 29 0.355 10 0.576 20 0.423 30 0.349 Select the correct answer below: T is significant because t is between the positive and negative critical values. r is not significant because it is between the positive and negative critical values. ↑ is significant because it is not between the positive and negative critical values r is not significant because it is not between the positive and negative critical values.
Transcript text: Suppose you computed $r=-0.235$ using $n=42$ data points. Using the critical values table below, determine if the value of $r$ is significant or not. \begin{tabular}{cccccccc} df & CV (+ and - ) & df & CV (+ and - ) & df & CV (+ and - ) & df & CV (+ and - ) \\ \hline 1 & 0.997 & 11 & 0.555 & 21 & 0.413 & 40 & 0.304 \\ \hline 2 & 0.950 & 12 & 0.532 & 22 & 0.404 & 50 & 0.273 \\ \hline 3 & 0.878 & 13 & 0.514 & 23 & 0.396 & 60 & 0.250 \\ \hline 4 & 0.811 & 14 & 0.497 & 24 & 0.388 & 70 & 0.232 \\ \hline 5 & 0.754 & 15 & 0.482 & 25 & 0.381 & 80 & 0.217 \\ \hline 6 & 0.707 & 16 & 0.468 & 26 & 0.374 & 90 & 0.205 \\ \hline 7 & 0.666 & 17 & 0.456 & 27 & 0.367 & 100 & 0.195 \\ \hline 8 & 0.632 & 18 & 0.444 & 28 & 0.361 & & \\ \hline 9 & 0.602 & 19 & 0.433 & 29 & 0.355 & & \\ \hline 10 & 0.576 & 20 & 0.423 & 30 & 0.349 & & \end{tabular} Select the correct answer below: $T$ is significant because $t$ is between the positive and negative critical values. $r$ is not significant because it is between the positive and negative critical values. $\uparrow$ is significant because it is not between the positive and negative critical values $r$ is not significant because it is not between the positive and negative critical values.
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Solution

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Solution Steps

To determine if the value of \( r \) is significant, we need to compare it to the critical value for the given degrees of freedom (df). The degrees of freedom can be calculated as \( n - 2 \). We then check if \( r \) is between the positive and negative critical values. If it is, \( r \) is not significant; otherwise, it is significant.

Step 1: Calculate Degrees of Freedom

Given \( n = 42 \), the degrees of freedom (df) is calculated as: \[ \text{df} = n - 2 = 42 - 2 = 40 \]

Step 2: Determine the Critical Value

From the provided critical values table, the critical value for \( \text{df} = 40 \) is: \[ \text{CV} = 0.304 \]

Step 3: Compare \( r \) with Critical Values

Given \( r = -0.235 \), we compare \( r \) with the critical values \( \pm 0.304 \): \[ -0.304 < r < 0.304 \] Since \( -0.304 < -0.235 < 0.304 \), \( r \) is between the positive and negative critical values.

Final Answer

\( r \) is not significant because it is between the positive and negative critical values.

\[ \boxed{\text{r is not significant because it is between the positive and negative critical values.}} \]

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