00:01
All right, so we're looking at tire treadwear on two brands of tires and they were all tested on the same car car one car two three four all the way down to car 12 12 different cars were tested with brand one and two and what we want to know is whether or not the we're looking at the differences and what we want to know is if the mean treadwear brand two if this is greater than brand one so, uh, we have the differences here, which is taken as b1 minus b2 brand one minus brand two and we're going to conduct a hypothesis test at the alpha of 0 .10 level of significance so let's state our hypotheses.
00:43
Oh before we do that let's just state that we're going to assume this population of differences is normally distributed.
00:48
That's all good.
00:49
So we're going to assume uh, no, it's it's normally distributed.
00:54
It was normal so we're going to go ahead and use our t -test for dependent samples or t -test for dependent samples, so let's say our hypotheses first.
01:07
So the null hypothesis would be uh, the mean difference we'll say mu sub d uh is going to be uh be zero the alternative hypothesis well, let's think about this if we want brand two if we're testing if brand two has greater tread more treadwear more treadwear here this is a bigger number these this difference would be negative.
01:34
So that means the mean difference would be less than zero.
01:37
Um now note on the null hypothesis.
01:41
I i initially said equal zero, but some professors say you know what these should be complementary events meaning you can only have one or the other so sometimes you might see this as the mean is greater than or equal to zero whereas that null the alternative is is strictly less than um, and depending just be clear with your professor which uh, which way they want you to to work how they want you to think about this because the real kicker the real the main thing is this that this you're looking for this thing being strictly less than zero but just for completeness just to make sure we're we have all of our of our uh, we're being as thorough as possible.
02:22
We'll do this complementary piece all right, so we'll say no is that the difference is greater than or equal to zero the alternative strictly less than all right.
02:33
So it's a we said earlier.
02:34
It's going to be a t test a test statistic and that formula is going to be the mean differences d bar uh the taking the differences and taking the average of them divided by s sub d the difference the standard deviation of said differences divided by the square root of n which is the number of samples so order of operations is important here.
02:56
This is the big division bar this whole term sds divided by root n that's the denominator.
03:01
Just be careful of that all right.
03:03
So let's go ahead and do that.
03:05
We've got our differences already b1 minus b2 and indeed the mean is negative uh, here's what we get.
03:11
Here's the whole t statistic as well...