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Suppose a relationship between two variables is found to be statistically significant. Explain whether each of the following is true in that case:

A) there is definitely a relationship between the two variables in the sample. B) there is definitely a relationship between the two variables in the population. C) it is likely that there is a relationship between the two variables in the population.

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For A) This is true (with a small questionmark). Since we restrict attention in the sample, I believe that the statement is true. Assume there was only the sample and no other unsampled units in the population. Then the statement would be true. But that is exactly what he means, since he restricts our attention only in the sample.
For B) This is definitely false. You make only inferences about the population based on a random sample, and you can never be "definitely" sure about any statement concerning the population. The only case you can definitely sure is in the case that you have sampled the whole population (is called inspection rather than sampling).
For C) This is true. That is exactly your conclusion.

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