00:01
For this test, we want to test the hypotheses that the mean is 69 .9 versus the mean is less than 69 .9 at a significance level of 0 .10.
00:15
And to do so, we have this information.
00:17
We know that the population standard deviation is 13 .5.
00:21
We also have a random sample of 25, which yielded a sample mean of 61.
00:27
So the first step is to find the test statistic for this test, and it's based on the standard normal distribution and that's because we know the population standard deviation.
00:41
It's given as the sample mean minus the null hypothesized mean divided by the population standard deviation over the square root of the sample size.
01:13
And this comes out to approximately minus 3 .296.
01:23
So now to find the p value based on the test statistic.
01:29
And we note that this is a left tail test.
01:32
We know that because if we look at the alternative hypothesis, it's a less than hypothesis.
01:38
And for a left tail test, the p -value is equal to the probability of having gotten a test statistic, at least as small as the one that we got...