00:01
So you've been given the null and alternative hypotheses.
00:06
Mu is greater than or equal to 20, and the alternative was that mu was less than 20.
00:15
You are also dealing with some given information about the sample size.
00:20
We are looking at a sample of size 50, and the mean of that sample was 19 .4, and the population standard deviation is equivalent to 2.
00:36
And in part a, we want to calculate the value of the test statistic for this hypothesis test.
00:47
So since sigma is known, we're going to be finding a z score as the standardized test statistic.
00:57
And we'll calculate that z score by substituting into the formula x bar minus mu -sacore.
01:03
Sub -h over sigma divided by the square root of n.
01:10
So that would be 19 .4 minus the mean that is described in the hypotheses of 20 divided by 2 over the square root of 50.
01:23
And you will get negative 2 .12, 13, 203436.
01:32
But your directions were very specific to round to two decimal places.
01:38
So we'll say negative 2 .1 .2.
01:42
Now for part b, you need to determine the p value.
01:46
And the p value is going to be an area.
01:51
So we're going to draw our bell -shaped curve, and we're going to draw a left -tailed test, and our z score was a negative 2 .1.
02:06
And we're trying to determine the area in this left tail and that would correspond to our p value so we could go to our standard normal z distribution in the back of your textbook and down the left side we would find negative 2 .1 which is going to be the ones and the tenths place of our z score and across the top we'll be looking for the hundredth place which is a and you're going to get an area of 0 .0170, and that is representing this area that is in that left tail.
02:45
And that is your p value.
02:48
And then it looks like the rest of the problem you did get correct.
02:53
So part c is saying using alpha at 0 .05, can it be concluded that the population mean is less than so this is asking us to actually run the hypothesis test utilizing our p value.
03:13
And since our p value is less than the level of significance, our p value is 0 .170, and it's less than 0 .05, our decision is going to be to reject the null hypothesis.
03:31
So by rejecting that null hypothesis, then you are supporting the alternative hypothesis, so it can be concluded that the population mean is less than 20...