Questions: After collecting n=20 data points, suppose you computed r=-0.85. 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. r is significant because it is between the positive and negative critical values. r is not significant because it is between the positive and negative critical values. r 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.

After collecting n=20 data points, suppose you computed r=-0.85. 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. r is significant because it is between the positive and negative critical values. r is not significant because it is between the positive and negative critical values. r 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: After collecting $n=20$ data points, suppose you computed $r=-0.85$. Using the critical values table below, determine if the value of $r$ is significant or not. \begin{tabular}{ccccccccc} \hline df & \begin{tabular}{c} CV + and \\ - \end{tabular} & df & \begin{tabular}{c} CV + and \\ - \end{tabular} & df & \begin{tabular}{c} CV + and \\ $-)$ \end{tabular} & df & \begin{tabular}{c} CV + and \\ $-)$ \end{tabular} \\ \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 & & \\ \hline \end{tabular} Select the correct answer below. $r$ is significant because it is between the positive and negative critical values. $r$ is not significant because it is between the positive and negative critical values. $r$ 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 correlation coefficient \( r = -0.85 \) is significant, we need to compare it to the critical value from the table for \( n = 20 \) data points. The degrees of freedom (df) is \( n - 2 = 18 \). We will check if the absolute value of \( r \) is greater than the critical value for df = 18. If it is, \( r \) is significant; otherwise, it is not.

Step 1: Determine Degrees of Freedom

To find the degrees of freedom, we use the formula: \[ \text{df} = n - 2 \] Given \( n = 20 \), we calculate: \[ \text{df} = 20 - 2 = 18 \]

Step 2: Identify the Critical Value

From the critical values table, for \(\text{df} = 18\), the critical value is: \[ \text{CV} = 0.444 \]

Step 3: Compare the Absolute Value of \( r \) with the Critical Value

We compare the absolute value of the correlation coefficient \( r = -0.85 \) with the critical value: \[ |r| = |-0.85| = 0.85 \] Since \( 0.85 > 0.444 \), the absolute value of \( r \) is greater than the critical value.

Step 4: Determine Significance

Since \( |r| \) is greater than the critical value, the correlation coefficient \( r \) is significant. This means that \( r \) is not between the positive and negative critical values.

Final Answer

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

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