00:01
Study in the journal of american medical association that reported the results of an experiment where 40 overweight individuals followed the atkins diet for a year and their weight changes at the end of the year had a mean of 2 .3 kilograms and standard deviation of 4 .7 kilograms.
00:19
And we're going to use this data to test the claim that the diet has an effect.
00:23
And so our null hypothesis will be that the mean of the differences is equal to zero and the alternative is that the mean of the differences is not, or is greater than zero.
00:40
All right.
00:41
And there's some criteria that need to be met for this to work.
00:47
And these are the criteria.
00:49
In order for us to test these conditions or test this set of hypotheses, we need to meet some criteria.
00:57
And these are the possibilities.
00:58
And so which of these five things have to be met in order to test this claim? so first off, this one, the sample size must be at least 30 or the population data for weight loss must be normally distributed.
01:10
That one.
01:11
It must be at least 10 people who succeed.
01:13
No, it's not a binomial scenario, so that's not it.
01:17
Independence.
01:18
We need to have an assumption of independence, meaning that one person's weight change does not have any impact on another person's weight change.
01:28
At least five people who follow the right for a year.
01:30
Nope, don't need that.
01:31
Again, that's kind of dealing with sample size, but it's not five.
01:35
We need at least 30.
01:37
Or the other one is that the weight loss measurements for people in the sample must be normally distributed.
01:43
This is kind of going along with a.
01:46
It's kind of this part of a.
01:52
Because if this is true, if the weight loss for the people in the sample is normally distributed, that gives us evidence to say that the population is normally distributed.
02:03
So a, c, e.
02:06
All right.
02:07
So now let's go ahead and do our test here.
02:11
So we're going to use the dependent samples t -test or paired samples t -test.
02:18
That's another way we can talk about it.
02:20
Paired samples.
02:21
And we get our test statistic by taking the mean of the differences, d -bar, minus this assumed population mean difference of zero, divided by the standard deviation of the differences, divided by the square root of the sample size.
02:37
So we substitute our values in.
02:39
We get the following t -score of 3 .095, we'll say, if we round to three decimal places.
02:46
To get the p -value, we use this t -dist function where you input the absolute value of your test statistic.
02:55
And this is in google sheets and excel.
02:57
This is our degrees of freedom, which we find by taking n minus one.
03:01
That's the degrees of freedom for a paired samples t -test.
03:04
And then one is the number of tails...