Why do we need to use degrees of freedom with the t distribution, but not the...

Why do we need to use degrees of freedom with the t distribution, but not the z distribution?

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Expert Solution

t-distribution is a type of sampling distribution which depend on the sample size. As we know Z distribution is applicable for large sample test i.e if sample size, n>30 then we use Z-test and the value of Z i.e. area of the standard normal curve doesn't depend upon the value of n, it only depends upon the α. But the value of t i.e. area of the t-distribution depends upon the value of n and α both and it is applicable whenever sample size, n≤ 30.

Basically, degree of freedom= sample size - 1 or total no. of data- no. of conditions

For example, the critical value of t at 15 degrees of freedom at α= 0.05 is 2.13 and if there is 18 degree of freedom, then the value of t at α= 0.05 is 2.10. But the critical value of Z at 0.05 level of significance is 1.96 and at 0.10 level of significance is 1.645, it doesn't matter the size of the sample.

That's why we need to use degrees of freedom with the t distribution, but not the z distribution.

orchestra answered 1 year ago

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