For this exercise, we are going to compute tail area probabilities, which we wil

Question

For this exercise, we are going to compute tail area probabilities, which we will use in earnest when we get to confidence intervals. Define the notation z_alpha to be such that P(Z z_alpha) = a, where Z is a standard normal random variable (Z~N(0,1)). A similar notation for the t distribution can be used, t_df alpha For example z_025 = 1.96 as seen in the picture below. For the normal distribution, this tail area is found using the Stata command: display invnorm(1 -alpha) For the t distribution with df degrees of freedom, this area is found using the command display invttail(df, alpha) Fill in the following table and comment on the results.

Explanation / Answer

Explanation:- From the table it is evident that as the level of significance decreases or the tail area increases the corresponding upper alpha th point also increases which is ofcourse trivial to undestand. From the standard normal and t table we find the points.

0.05 0.025 0.005 Z 1.645 1.96 2.576 t(10) 1.812 2.228 3.169 t(30) 1.697 2.042 2.75 t(100) 1.66 1.984 2.626 t(1000) 1.646 1.962 2.581

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