00:01
All right, here we have a local health department conducted a study to determine whether the average number of annual doctor visits for people living in a rural area is different from the national average of 3 .5 visits per year.
00:11
A sample, a random sample, so our m here is going to be equal 60.
00:16
So m is equal to 60.
00:18
That's our random sample.
00:19
Now, this is important because it's more than 30.
00:22
That means we can use the z test because the central limit theorem is going to be satisfied.
00:27
All right, so we have that their average number, our x bar, is equal to 3 .2, and their sample standard deviation is 1 .1.
00:35
Okay, and we need a 5 % significance level.
00:39
I'm going to interpret that as a 95 % confidence interval.
00:42
Those are equivalent.
00:43
They mean the same thing.
00:46
So what we're going to do is a z test.
00:48
We're going to do a standard z test, and again, that's because our n is greater than or equal to 30, which means that the central limit theorem applies.
00:56
So we can use a z test because no matter what it is, it's a process.
01:00
Normally distributed, no matter if the population it pulled from is also not uniformly distributed, but normally distributed.
01:11
Okay, so what we're going to do is we're going to create a confidence interval, but first we need to determine what our null hypothesis is and our alternate hypothesis is.
01:20
Our actual hypothesis, or our null hypothesis is that our mu is actually equal to what they say it is, which is what, 3 .5, right? okay, so 3 .5.
01:32
And then we're saying, no, we think that the mu is different from 3 .5, which tells us that we're making a two -tailed test.
01:40
Okay, so what we're going to do is we're going to say we have our formula for a confidence interval, which is x bar, plus or minus a z score that's associated with 5 % significance or 95 % confidence interval.
01:52
And then we're going to multiply that times our standard deviation divided by the square root of our sample size.
01:58
So we're going to say x bar.
01:59
We know what that is.
02:00
That was 3 .1, or 3 .2.
02:03
What was it? let me scroll back up.
02:05
I have it written 3 .2.
02:08
Okay, so that's 3 .2 plus or minus.
02:12
Rz score for a 95 % confidence interval is 1 .96.
02:16
I just have that memorized.
02:17
I've used it a thousand times.
02:19
So it's always the same.
02:21
You can look it up on your table or you can just look it up online.
02:25
But it's going to be 1 .96.
02:26
So our standard deviation is 1 .1...