A simple random sample has a sample size of n = 65. Given the population is normally distributed, find the critical value ta/2 corresponding to a 99% confidence level. I know the answer is 2.660, but I’m confused on how to get there.

In your t-table look for the row containg 64 degrees of freedom because dof=n-1. Find the 2-tail column for 0.01, at the row-column intersection you find the figure 2.660 (or approximately so depending on the accuracy and scope of your table).

We use 2-tail figures t(ɑ/2) when we’re testing for equal/not equal, otherwise we want 1-tail—the left tail of the normal distribution for less than (or less than or equal) or the right tail for greater than (or greater than or equal). That’s why the columns have two different labels, depending on what condition you are testing.

The significance level ɑ and the confidence level are related. 0.01 significance (1%) is the same as 0.99 (99%) confidence level. The two always add up to 1 (100%).

by Top Rated User (763k points)