00:01
So for this problem, our first task is going to be to find our sample mean value, x bar, which we do by adding up each one of the individual data points and then dividing by the sample size.
00:14
So x bar is going to be 73 plus 70 plus 67 plus 63 plus 67 plus 72.
00:26
Divided by, you have one, two, three, four, five, six data points.
00:30
So our sample mean value is going to come out to roughly 68 .67.
00:37
Then, to find the margin of error that's equal to z for a proportion of 1 minus alpha over 2 times our population standard deviation divided by the square root of our sample size.
00:55
We can find, well, actually i'll point out specifically, one second here, that z for 1 minus alpha over 2 is, is going to be equal to z for a cumulative proportion to the left of 0 .995, which is equal to about 2 .576.
01:15
So our margin of error is going to be 2 .576 times population standard deviation of 2 inches, divided by the square root of 6, which will give us a margin of error here of roughly 2 .1033...