00:01
Hey there, welcome to numerate.
00:02
We are asked to find the critical value based on this distribution that the statistics shows here so we're trying to find the critical value for this confidence interval basically.
00:13
So with this, we had to first figure out this is a t distribution or a z distribution.
00:19
So let's write what we're given over here.
00:22
We're given a sample size of 232 we're also given an x value here of 31 .3.
00:31
And we're given a standard deviation of 6 .3.
00:37
So let me just cover one of them.
00:40
So we use a z distribution.
00:49
We use a z distribution when we're giving them population standard deviation or when it's normally distributed, when it says it's normal with a sample size that is greater than equal to 30.
01:03
So we have our sample size, a large sample size, but we're not given that it is normally distributed the population so therefore we will use a t distribution here so with this we have our confidence interval here a confidence level of 0 .95 meaning that our alpha level here is 1 minus 0 .95 which is which is 0 .05 and we're going to divide by 2 because confidence intervals are two -tailed, so 0 .025 would be our true alpha level here.
01:56
And what we're searching for, what we're looking for is t of alpha divide by 2.
02:01
Right, so it will basically be equal t of 0 .025...