00:01
There are given data here and the number of data here is 10.
00:06
So we need the mean score for the sample.
00:10
So we're going to find this one.
00:12
And the standard deviation also.
00:14
We need these two values in order to get the confidence interval.
00:21
So first of all, let's find the mean.
00:23
So in order to find mean, i'm going to just add those 10 numbers and divide by 10.
00:29
But instead of just adding all of them by hand i'm going to use the calculator just press the stat and edit enter so i'm going to just clear all the value here the first one is 25 .2 and the next one is 21 .3 and the next one is 22 .8 the next one is 17 and the next one is 29 .8 and the next one is 21 .9 grade and the next one is 21 .9 grade and the next one is 25 .5 and the next one is 16 and the next one is 20 .9 and 19 .5.
01:10
Great.
01:11
So we got all the values here.
01:13
In order to get the mean and the standard division again, press the button stat.
01:18
On the calculation tab there is a one variable statistics, just press enter.
01:22
And we got the mean value here.
01:25
So we got the mean, which is denoted by x bar, that is 21.
01:30
Let's say this is 99th and the standard deviation which is 4 .12 so we got these values and for part a we have to just find the confidence interval for the population mean the confidence interval for the population mean which is x bar plus or minus so we don't know the population standard deviation since we have to use because of that we have to use the t distribution.
02:05
This is t alpha over 2 and times the standard deviation divided by square root of the sample size.
02:12
So first of all let's get the alpha over 2 here.
02:15
So the alpha which is one minus the confidence level.
02:19
So by the way the confidence level is given as 0 .95 here which is 95%.
02:24
And that means the alpha over 2 which is 1 minus 0 .95 and divided by 2, that is 0 .0 .25.
02:36
Great.
02:38
No, actually, this is 0 .025.
02:41
Let me just check this value here.
02:43
This is 1 minus 0 .95 and divide by 2, and we got 0 .025.
02:50
Great.
02:50
So what is the t value and the degree of freedom, which is equal to n minus 1? so totally there are 10 numbers here.
02:58
The degree of freedom is 10 minus 1, 9.
03:02
So the t 0 .025 and the degree of freedom is 9 here.
03:07
I'm going to use the inverse t property of the tic calculator.
03:12
The aria is 0 .025 and the degree of freedom is 9.
03:16
So just press the button second and distribution there is inverse t here.
03:22
The area is 0 .025 and the degree of freedom is nine.
03:26
So we got the value as negative 2 .2, 6, 20.
03:31
2.
03:32
Great...