00:01
So we're looking at a test that's being performed.
00:03
A brand of tyres claims that its deluxe tyre averages at least 48 ,000.
00:11
So we want to test that claim.
00:13
Okay, so if we look at the hypotheses, i'd love to put mean is at least 48 ,000.
00:21
That would be a great claim here.
00:22
But the sample mean that we are looking at is greater than this point.
00:28
So instead i'm going to look at the opposite claim, that it's 48 ,000 or is greater.
00:38
Not ideal because their claim is at least, but if we use the other one there's no case in which we would reject the null hypothesis.
00:47
Our sample size is 28, 48, our sample mean is 50 ,000, and our sample standard deviation, 9 ,800.
00:57
We want the test value, the test statistic.
01:01
So we start by assuming that the null hypothesis is true.
01:06
Pretend the mean is 48 ,000.
01:08
And look at the distribution of sample means that would produce.
01:14
The sample size is a little small for this, but we can use a normal approximation here, using the central limit theorem, and that would say that the sample means follow a normal curve, mean same as population mean, standard deviation, sigma over root n, where sigma is the population standard deviation...