00:01
In the given question we are told that the administrator at your local hospital states that on weekends the average wait time for emergency patients is 10 minutes.
00:12
And based on the discussions you have had with friends who have complained how long they waited to be seen in the year over a weekend, you are disputing the administrator's claim and over a course of few weekends you are recording the wait time for 40 patients and you have complained.
00:30
Found that the average wait time was 11 minutes with a standard deviation of 3 minutes.
00:35
Now we are told to use a level of significance of 5 percentage to test this claim.
00:42
So what we can do first is to state the null and alternative hypothesis.
00:47
The null hypothesis would be that it is equal to 10 minutes and the alternative hypothesis would be that it is not equal to 10 minutes.
00:56
And now to calculate the test statistic, what we can do over here is we can take the z value, which is a test statistic, which is calculated by taking x bar minus mu divided by the standard deviation divided by the square root of the sample size.
01:17
We know all these values.
01:19
The sample mean is 11.
01:21
The assumed mean is 10 minutes.
01:23
The standard deviation is 3.
01:25
And the square root of the sample size would be square root of 40.
01:30
On evaluating this, we get the z value over here to be equal to 2 .108, which we can approximate as 2 .11, right? so the z value is approximately 2 .11.
01:50
And this is the value of the test statistic that we have found.
01:55
So now what we can do is we can take the p value and to find the p value for a two -tailed test, what we would do is in a normal distribution curve, we would take the part where our z value is, that is in this curve, the central value is where z equal to zero.
02:25
So we would take the points where z is equal to 2 .11 and the negative value as well, that is z equal to negative 2 .11.
02:38
And the area towards the left of negative 2 .11 and towards the right of the value of positive 2 .11 is what we would have as the p value over here.
02:53
So to find the p value, what we would do is that we would take the p value is equal to 2 times the probability.
03:03
We just have to find the probability of either of these regions...