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The alternative hypothesis in a test of a correlation coefficient states that a true relationship does exist between the variables within the target population. It is mathematically expressed as $$ho 
eq 0$$, representing any non-zero population correlation.

Alternative Hypothesis for a Correlation Test

A hypothesis test of the correlation coefficient can be structured as either two-tailed or one-tailed. A two-tailed test is utilized when a researcher has no prior expectation regarding the direction of the relationship, whereas a one-tailed test is selected if a specific directional relationship (either strictly positive or strictly negative) is anticipated.

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