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I have a moderate correlation, but my chi square rejects alternative hypothesis

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I am doing my Math studies IA on the relationship between two variables and I have a moderate positive correlation, but after I did my chi-square test my chi-square value was smaller than my critical value, where I have to reject the alternative hypothesis which concludes that the variables are independent of each other. Is this possible or am I wrong?

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Check the formula or spreadsheet you are using by repeating the test on a textbook problem for which you know the answer. 

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