00:01
For this question, there is a sample size.
00:03
So we don't know the sample size, but let's say the sample size denoted by n and the standard deviation.
00:10
So the standard deviation, let's say this is the population standard deviation, which is sigma.
00:15
This is the population standard deviation.
00:18
And the mean value, which is x bar, this is the sample mean.
00:24
And the confidence level.
00:26
So we have two confidence levels.
00:27
The first one is 95 percent and the second confidence level, which is 90 percent.
00:33
When we just decrease the confidence level, so what about the confidence interval? let's remember the confidence interval formula.
00:42
So the confidence interval for mean, which is the sample mean, plus or minus the z value, times the population standard deviation and divided by square root of sample size.
00:54
So these yellow highlighted parts are all the same.
00:58
So what is important to just decide if it is decreasing or increasing? the z value here.
01:05
Let's take a look at the z value.
01:07
So the alpha is 1 minus confidence level.
01:10
We need alpha over 2, which is 1 minus 0 .95, divided by 2, which is 0 .025 here.
01:16
Let's get the z alpha over 2, which is, i'm going to use the inverse norm function here.
01:21
So the area was 0 .025, the mean and the standard deviation...