00:01
Here we have a sample of size 20, which yielded a sample mean of 20 and a sample standard deviation of 2.
00:07
We are asked to find the t value that would be used for a 95 % confidence interval for the population mean.
00:15
Now the t value is sometimes denoted t sub alpha over 2 with n minus 1 degrees of freedom.
00:24
Because we want 95 % confidence, this means that alpha is 1 minus .95, which is .05.
00:30
And so the t value is t sub .025 with n minus 1 or 19 degrees of freedom.
00:43
And what this notation means is, well the 19 means it's the t distribution with 19 degrees of freedom.
00:50
But graphically, if this is our t distribution with 19 degrees of freedom, t sub .025, let's say it's here, is the t value such that there is an area of .025 in the tail to the right of it.
01:06
So one way to find this value is to go to the t table, find the row that corresponds to 19 degrees of freedom, and use the column that corresponds to an area of 0 .025 in just one tail, the right tail, and this gives us a t value of 2 .093...