00:01
So in this question, we have an automobile manufacturer that gives itself a 31 .8 miles per gallon rating.
00:11
In tenant testing, we take 210 samples of the van and we get a sample mean of 31 .7 and the population standard deviation is known at 2 .6.
00:28
The question is we want to look at a 0 .05 level, 5 % significance level to support the, see if the claim is supported.
00:36
So i mean, your prior here should probably be that it looks like it is likely going to be supported, but let's go through and check.
00:46
It's possible.
00:47
There's a lot of samples, so it's possible.
00:50
There's a surprise here, but the, right, our, our null hypothesis here is going to be, we're hypothesizing on the population mean.
00:58
So null hypothesis is that the population mean is 31 .8.
01:03
The alternative is we're just going to test their claim.
01:10
So that it's not 31 .8.
01:14
We then are interested in finding the value of the test statistic.
01:20
And remember for this, the test statistic is basically just a z score calculation.
01:25
So you just go and we compute x bar minus mu divided by, and then we want the standard deviation of our sampling distribution, which is sigma over root n...