We lose one degree of freedom in calculating sample standard deviation because sample mean is used, why do we lose one degree of freedom in one sample t-test?
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They are not same. We use t test when when we infer something about the population from the sample. When we calculate this we lost the freedom of including population for the calculation hence we lose one degree of freedom.That's why we use n-1 instead of n.
These freedoms can be more than one. So t test and losing degree of freedom are not same.