00:01
Hey there, welcome to numerade.
00:03
So we are asked to construct a confidence interval here and find the appropriate critical value based on the distribution that is shown through the histogram and statistics here.
00:14
So let's first write what we're given.
00:16
We're giving a confidence level of 0 .99 converted to decimal form.
00:30
With this confidence level, we can find our significance level, which is basically 1 minus our confidence.
00:36
Level and this will equal around 0 .01 but for our alpha level we have to divide by two since we are dealing with a confidence interval here looking at both sides so 0 .01 divided by 2 equals 0 .005 for our alpha level all right and with that we are also given our population standard deviation so we are given that so check mark and we are given the sample size here sample size here is 57 now let's go back to the population standard deviation since we are given the population standard deviation this implies we're going to use a z distribution all right so our z critical value we can denote it as z subscript 0 .005 there's going to be two possible answers our z critical value or it will be neither.
01:53
This depends on what is the shape of the curve.
01:57
If it's normally distributed, then it would, we will use a z critical and we will use a z distribution.
02:03
So a normal curve looks like this.
02:06
So on your histogram, it's not that curve, but if you, the histogram is basically little blocks next to each other, but if you would draw a line, it will be like a normal curve, right? and if you look at histogram, if it is skewed in any way this time...