00:01
The following is the solution to number 49, and this just looks at three different data sets that are very, very similar.
00:07
Just the sample sizes are a little bit different.
00:10
And this is taken from a population where the mean is 100, and the population standard deviation is 15.
00:16
So we're going to do a few z intervals.
00:17
But the first part of this is to find the sample means for each dataset.
00:21
And i did technology.
00:22
I used technology for this.
00:24
So i use a t -i -84 because it really cuts down, especially as the datasets get bigger.
00:28
But you can use any sort of technology.
00:30
Excel works great, mini tab, or you can do the formula.
00:35
It might take you a little longer, but that's fine too.
00:37
So stat and edit, and you see i have these three datasets here, and i'm just basically going to do the dataset x bar for l1, l2, and l3.
00:45
These are my three different datasets.
00:48
So stat, and then arrow over to calc, and it's the one bar stats.
00:52
And i'll just go ahead and change that to l1, and this is my first x bar, x1 bar 99 .125.
01:01
So x1 bar is 99 .125.
01:05
So i do the same thing, go to stat, calc, one bar stats, but this time it's going to be l2, so the medium data set, and i get about 99 .1.
01:16
99 .1 for x bar.
01:19
And then very last, go to stat, calc, one bar stats, and then i'm going to change this to l3, and that's about 90 .03 repeating.
01:31
So we'll say 90.
01:33
I'm sorry, 99 .03.
01:35
So you can see these sample means they're roughly the same.
01:38
They're maybe slightly off by a couple hundredths, but it's not huge, right? so you can essentially think, okay, these are about the same sample means.
01:48
So now we're going to do the 95 % confidence interval for each one of these, and we're going to compare.
01:53
So let's take a look.
01:54
If we go to stat and then tests, now, since we know the population standard deviation, we can use the z interval.
02:01
And we have data, since we're given a list of data, the sigma is 15, and i'm just going to go in order.
02:08
So my list is l1 first.
02:10
The frequency is always one, and then the c level, the confidence level is 95%.
02:14
So 0 .95.
02:15
And then i go ahead and calculate.
02:17
And this top one here, that's my confidence interval.
02:20
So it's a pretty big confidence interval.
02:21
And that's 20 -ish, maybe a little more than 20 units apart.
02:26
So let's go and write that down, 88 .731, 88 .731, all the way up to 109 .52.
02:38
So that's whenever the data set was quite small.
02:40
It was about eight data values, i think.
02:41
So we're going to do the same thing.
02:43
If we go to stat and then tests, and it's that seventh option again.
02:47
But this time, we're going to go to l2.
02:52
So the medium data set size, and let's see what happens here.
02:55
So 92 .526 all the way up to 105 .67.
03:00
So you see it's already getting a little bit smaller.
03:01
It's about 13 units apart as opposed to 20.
03:04
All right, so 92 .526 all the way up to 105 .67.
03:16
And then finally, the last dataset, so that's whenever n equals 20.
03:22
So stat tests, and it's still the seventh option.
03:25
But this time it's going to be the third column.
03:29
And let's see what happens here.
03:31
So this is where the sample size was 30.
03:33
93 .666 to 104 .4.
03:36
So you see that's even smaller...