00:01
For this question, there is given 10 data here.
00:04
So what we need for the confidence interval.
00:08
So first of all, what is given here? so we need the mean value, so the mean of the sample.
00:16
So mean of the value here, let's say this is x bar.
00:20
And so we need the standard deviation, which is denoted by, let's say, this is s.
00:28
And the sample size, so the n, which is given as 2.
00:31
200 here and what about what about the confidence level here so the confidence level which is given as this is 95 confidence interval so that means this is 0 .95 here so we have to use the t method here that means we need to use the t distribution and actually so the so the sample actually the sample is given as 10 here so i'm going to write as 10 because there are just only 10 values here so we have to just construct on the confidence interval let's remember the formula the confidence interval c i which is equal to x bar plus this is t alpha over two times standard division divided by the square of n here so first of all let's get the alpha value here so the alpha is one minus confidence level that means the alpha over two which is 1 minus 0 .95 and divided by 2 which is 0 .025 and the degree of freedom.
01:33
So the sample size is given as 10.
01:36
So this is n minus 1.
01:38
So the degree of freedom, which is 10 minus 1, which is 9.
01:42
And also, we have to get the value here.
01:45
So the t value, so we're going to use the inverse t function.
01:49
The area is 0 .025, and the degree of freedom is 9.
01:52
So from here, let's get the z value.
01:55
So for inversity, just press second and distribution, there is inverse t here.
02:01
And the area is 0 .025.
02:03
The growth freedom is 9.
02:05
So we got the value as this is negative 2 .26 and 22.
02:10
Great.
02:11
So we got this value here...