As the degrees of freedom increase how does the t subscript

As the degrees of freedom increase, how does the t subscript alpha over 2 comma n minus 1 end subscript value compare to the z subscript alpha over 2 end subscript value?

Solution

Degree of freedom increases means sample size incraeses. As the sample size incraeses, sample standard devaition comes closer to population standard deviaiton. That is distribution of t becomes closer to distribution of z. That is as the sample size incraeses t-critical value comes closer to z critical value for same information.