00:01
To construct confidence intervals, we'll need to know the sample mean.
00:06
So you can add up the 6 and divide by 6, it's 5.
00:10
And we'll need to know the sample standard deviation, which you can calculate with a statistical calculator, find the variance, the difference between all the elements and the mean, squared, add them up, divide by m minus 1.
00:25
It ends up being exactly the square root of 5 .2, which is about 2 .28.
00:32
So, for a 90 % confidence interval for the population mean, we do confidence intervals as the sample mean, plus or minus the margin of error, which is going to be the critical t, because this is a small sample, times the sample standard deviation, or the square root of the sample size.
01:00
And so, 5 plus or minus, there are 6 elements, so the degrees of freedom is 1 less than that at 5.
01:08
Alpha, in this case, is .10.
01:12
And so our critical t, with 5 degrees of freedom, using the student t distribution to find this, that table or a calculator, with 5 degrees of freedom, a significance of .1 is 2 .105.
01:43
And you want this, it doesn't say how many decimal places, so i'm going to go with 2.
02:01
So we have the lower boundary, 5 minus 2 .105 times the standard deviation over the square root of the sample size, is 3 .04, to an upper boundary from adding, which is 6 .96.
02:30
Then we want to go to a 95 % confidence interval.
02:36
So that would be the sample mean, plus or minus.
02:38
Now, alpha is .05, and our critical t becomes 2 .571.
02:56
Now our lower boundary becomes 2 .61, and our upper boundary 7 .39...