Question

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.

Step 1

From the given information, the sample size n = 25.

Therefore, the degrees of freedom is n – 2 = 25-2 = 23.

The correlation coefficient is -0.558.

From the given table, corresponding to the 23 degrees of freedom, the critical value is ±0.396.

Step 2

*Rule for the significant r:*

- If the correlation coefficient, r is not between the two critical values that is not between the negative and positive critical values, r is significant.
- Otherwise, r is insignificant.

Here, -0.558<-0.396.

That is, the correlation coefficient is not between the two critical values, -0.396 and 0.396.

Therefore, r is significant.

It can be shown as below,

Step 3

Therefore, the third option is correct that r is significant because it is not between the positive and negative critical values.

1st option is contradictory of 3rd option, hence, 1s option i...

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