Exercise: Head circumference and height, answer 5

Question 5: The significance test of the null hypothesis r = 0 in this population gave P < 0.0001. What does this mean and what precisely is it testing? How would you interpret the results of this test?

Suggested answer

P<0.0001 means that in the population which this sample of students represents, the probability of getting a value for the correlation coefficient as far or further from zero as is 0.40 is less than 0.0001. This is very unlikely event and the data are not consistent with the null hypothesis that in the population the correlation coefficient is zero.

The correlation being zero would mean that there was no linear association, no tendency for head circumference to be higher for taller students. We can conclude that there is very strong evidence that head circumference and height are related.

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