00:01
For this problem, to begin, we know that we are looking to find the lower bound of a 90 % confidence interval for the population mean.
00:07
So that's going to be given by our sample mean value minus, since we have a small sample and an unknown population standard deviation, we use a t -statistic for n -1 degrees of freedom and a one -tail proportion, or a p -value of 0 .05, multiplied by our sample standard deviation divided by the square root of the sample size.
00:28
Now, as you can see in the bottom corner there, i've calculated the sample statistics ahead of time here, just to save a little bit of time, since the focus here is more on creating the confidence interval rather than the more basic, straightforward aspect of finding the sample statistics.
00:44
I'll note that our sample mean value we find by taking the sum of each value divided by the number of values, find that the sample mean is 3 .8, and the sample standard deviation deviation, we find by taking the square root of divided by , which we find to be 1 .6193...