00:01
For this problem, you're told that a psychologist would like to test whether there is a relationship between depression and aging.
00:06
For the general population of adults, it is known that the mean depression test score is 40 with a standard deviation of 10.
00:13
So i'll note that those are the population mean and the population standard deviation.
00:19
We're then told that it is also known that depression scores follow a normal probability distribution.
00:26
So we're told that the psychologist took a random sample of 28 individuals who are, older than 70 years of age.
00:32
Now because n equals 28, that's less than the sort of cutoff point of 30.
00:38
That means that we're going to have to use a t test here.
00:43
So 28 individuals, we're told that the average depression test score of this sample is 43 .5.
00:51
So our x bar here is 43 .5.
00:55
For part a, we're asked to set up our null and alternative hypotheses to test the claim that the elderly people, or that the elderly people are more depressed.
01:03
So the null hypothesis would be that the population mean for elderly people is equal to 40, the result for the typical or for the general population.
01:19
The alternate hypothesis, specifically in this case where the hypothesis, you know, we've hypothesized that the, that depression increases, the alternate hypothesis would be that mu is greater than 40.
01:31
For part b, we're asked to compute the value of the test statistic.
01:36
So our test statistic, the t score here, is going to be x bar minus the null hypothesized mean value, divided by the known population standard deviation over the square root of n, the sample size.
01:50
So i'm just going to bring up the software that i use for crunching numbers here.
01:55
One moment.
01:56
I'll have to pause the recording.
01:58
All righty.
01:58
So we have that our x bar, 43 .5.
02:03
The null hypothesized mu is 40.
02:06
A standard deviation is 10.
02:09
And we divide that by the square root of n28.
02:12
So we get a t score here of 1 .852 roughly.
02:15
It says two decimal places.
02:18
Yeah...