00:01
Alright, so this is an interesting problem where we've been given that suppose if mu1 and mu2 are stopping distances at 50 miles per hour for cars of a certain type.
00:13
So it's been given that you sample are true mean stopping distances for cars of a certain type equipped with two certain braking system.
00:22
So let's say this is braking system a and this is braking system b and now you have to basically calculate a 95 % confidence interval for the difference of the average stopping distances for cars equipped with system 1 and system 2.
00:38
Okay, my bad.
00:39
I call this a and b.
00:41
This is, let's say system 1 and this is system 2.
00:45
Okay, and so essentially what we have to do is calculate a 95 % confidence interval for the difference of the means.
00:54
So x -hat minus y -hat.
00:56
What i'm going to do is go ahead and write what the formula is for the confidence interval and okay let's go about it.
01:07
So the confidence interval, i've already written the alpha value as you can see and let's mention the degrees of freedom which in this case are just 7.
01:21
Okay, so the confidence interval is essentially x -hat minus y -hat plus or minus t times square root of s1 square over n1 plus s2 square over n2.
01:51
Okay, now we've been given all the quantities already in this and okay i'm gonna have to calculate this out a little bit slowly.
02:20
So what we do firstly is we note what the value of t is.
02:25
So t is given a two -tail test at 0 .05 and 7 degrees of freedom is equal to, let me just look at the table really quick.
02:37
So 0 .05 for a two -tailed test at 7 degrees of freedom is 2 .365...