Question

When testing whether the correlation coefficient differs from zero, the value of the test statistic is t20 = −2.95 with a corresponding p-value of 0.0061. At the 5% significance level, can you conclude that the correlation coefficient differs from zero?
A) Yes, since the p-value is less than 0.05.
B) Yes, since the absolute value of the test statistic exceeds 0.05.
C) No, since the p-value is less than 0.05.
D) No, since the absolute value of the test statistic exceeds 0.05.

Answer 1

Answer:

A. Yes, since the p-value is less than 0.05.

Step-by-step explanation:

For the testing of correlation coefficient the null hypothesis and alternative hypothesis can be stated as

Null hypothesis: The correlation coefficient doesn't differs from zero.

Alternative hypothesis: The correlation coefficient differs from zero.  

If our p-value is less than significance level α then the null hypothesis will be rejected. We are given that p-value=0.0061 and α=0.05.

As we can see that p-value is much smaller than α, so, the null hypothesis will be rejected and we conclude that the correlation coefficient differs from zero.

So, the correct option is option A which is "Yes, since the p-value is less than 0.05".