00:01
For this question, they are given a sample.
00:03
And so the sample size here is 9.
00:06
So they are given nine numbers.
00:09
So what we need to get the confidence interval, we need the sample mean, which is denoted by x bar.
00:15
And also, we need the sample standard division.
00:17
So i'm going to get these values using the calculator.
00:19
So the first step, i'm going to put all those nine numbers on the calculator.
00:22
So press the button stat, stat, and then edit, enter.
00:26
So i previously put those nine numbers on the calculator.
00:29
Just save some time.
00:32
And then the next step, press the button stat, and the calculation tab, one variable statistics, and hit the enter.
00:39
So the sample mean here is which is 1 .01 with two decimal places.
00:45
And the sample standard division, which is sx value here, this is 0 .0.
00:52
Let's say this is 2 and 5.
00:54
This is the sample standard division.
00:56
So for the part a, the confidence level was given as 99%.
01:00
So we're going to find the confidence interval.
01:02
Let's remember the formula.
01:04
The confidence interval for the population mean, which is the sample mean plus or minus.
01:09
Because we know the sample standard division, so we have to use the t distribution at this step.
01:14
This is t alpha over 2.
01:16
And then sample standard division divided by square root of the sample size.
01:21
Let's get the alpha over 2 value.
01:23
So the alpha is, which is 1 minus confidence level.
01:26
But we need alpha over 2, which is 1 minus 0 .99, means 99%.
01:32
And then the t distribution, which is the sample size divided by 2, which would be 0 .05.
01:35
And also we need the degrees of freedom, which is n minus 1.
01:38
So this is 9 minus 1, which is 8.
01:40
To get the t alpha over 2, i'm going to use the graphing display calculator application, inverse t.
01:46
So the area was 0 .005 and the degrees of freedom, which is 8 at this step.
01:51
Press second variance and the inverse t.
01:54
This is 0 .005.
01:56
And the degrees of freedom, which is 8 here.
01:58
So the value here, which is negative 3 .36.
02:01
Let me just put these values on the formula.
02:03
The sample mean, 1 .01.
02:05
This is plus or minus.
02:08
3 .36 n times the sample standard division and divided by square root of the sample size, which is 9 here.
02:15
This is 1 .01 plus 3 .36 times 0 .025 divided by square root of 9, which is 3.
02:24
So the upper boundary for this question would be 1 .038...