What happens to a Student's t-distribution as the degrees of freedom increase? a.A student's t-distribution diverges...

What happens to a Student's t-distribution as the degrees of freedom increase?

a.A student's t-distribution diverges from the standard normal distribution as the degrees of freedom increases

b.A student's t-distribution converges to the standard normal distribution as the degrees of freedom increases

Solutions

Expert Solution

Answer :

A student's t-distribution converges to the standard normal distribution as the degrees of freedom increases.

This can be observed by comparing Z table and t table.

Z-Table :

Note that, Z-table gives the left tailed probability for corresponding Z-score.Consider the Z-score "1.65" at probability "0.9505".

t-Table :

Note that the t-Table gives the right tailed probability for the corresponding t-values. And hence in the "one tailed area" row at the top of the t-Table the probability "0.050" means the right tailed probability to the corresponding t-value. So left tailed probability is "0.950".

So Observing the column "0.050" in row "One-tail area" it is clear that as degrees of freedom increases the t-value corresponding to "0.050" converges to 1.65.

orchestra answered 1 year ago

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