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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.

Respuesta :

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".

akposevictor

The p-value (0.0061) is less than the significance level (0.05). Accept the alternative hypothesis.

We can therefore conclude that, the correlation coefficient differs from zero (Option A)

When testing an hypothesis, note the following:

  • Null hypothesis states that the correlation coefficient is zero (doesn't differ from zero).
  • Alternative hypothesis states that the correlation coefficient differs from zero.
  • Accept the null hypothesis if the p-value is greater than the significance level, then reject the alternative hypothesis.
  • Reject the null hypothesis if the p-value is greater than the significance level, then accept the alternative hypothesis.

Given:

p-value = 0.0061

significance level = 0.05 (5% significance level)

Thus, the p-value (0.0061) is less than the significance level (0.05), therefore, we would reject the null hypothesis and accept the alternative hypothesis.

We can therefore conclude that, the correlation coefficient differs from zero (Option A)

Learn more about correlation coefficient here:

https://brainly.com/question/9906772

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