00:01
The manager of a restaurant believes that the average customer satisfaction score is greater than zero.
00:06
So he believes the mean is greater than zero.
00:09
That would be the alternative hypothesis.
00:11
The null hypothesis would be it's not.
00:13
It's zero or lower.
00:15
I know which is which because a null hypothesis always has an equal sign.
00:21
So this must be the null and the claim must be the alternative.
00:25
We have a sample of size 20.
00:29
The sample mean is 2 .21.
00:34
The sample standard deviation is 4 .717.
00:39
We want the p -value.
00:42
So we need to look at the sampling distribution.
00:45
If we took every sample of this size, took the sample means and plotted them out, what would we get? well, something approaching a normal curve.
00:55
And its mean is the same as the population mean.
01:03
Its standard deviation is sigma over root n.
01:07
We've got the n for normal.
01:10
Sigma is the population standard deviation.
01:13
We don't have that.
01:14
All we have is the simple standard deviation.
01:17
Because of that, we cannot just use z, the standard normal variable.
01:21
We have to use t instead.
01:23
So t accounts for this uncertainty of not actually having sigma.
01:28
So what we're going to do is find the test statistic and then we'll find the p -value.
01:34
This is a one -tailed test.
01:36
We only care if our sample mean is significantly above zero.
01:39
We don't care if it's below.
01:41
So we're going to find the test statistic, which is going to be up here somewhere.
01:45
And the area beyond it is our p -value.
01:49
The p -value is the probability of getting a value like this or more extreme if the null hypothesis is true.
01:58
So this is going to use zero as the mean here, and we're going to find this area.
02:05
So first, the test statistic is basically the z -score for this value.
02:12
A z -score tells you how many standard deviations away from a mean this value is for this particular distribution.
02:19
The raw value is x -bar...