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I wrote:

Therefore, we reject the null hypothesis stating that these variable are independent.

The null hypothesis is "The variables X and Y are independent". Using a hypothesis testing we decided to reject this hypothesis. Could I write the sentence above as:

Therefore, we reject the null hypothesis that these variable are independent.

In general, can I use "that" instead of "which states that" or "which says that" or "which shows that" ...?

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    Whoa there. Stating and which states mean two different things, and vastly change your first quote section! Which states explains what the null hypothesis is, but stating indicates that you state something while rejecting the null hypothesis. The explanation below makes it clear you mean which states and that your second quote would be accurate for what you really want to say. – Smock Jun 27 at 14:01
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Yes, you may say

Thus, we reject the null hypothesis that these variables are independent.

A hypothesis is a type of statement so we can dispense with "stating" or "that states" as redundant.

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