00:01
In this question, we want to compute the confidence interval for the mean and also for the proportion.
00:06
So if n is large, n is the sample size.
00:10
And we know the standard deviation sigma in the population.
00:15
We can use this formula to compute the confidence interval for the mean, which z is the z score that we have in this table.
00:24
And the z score depends on the confidence level of each interval that we need to calculate.
00:32
For the proportion, we also have a formula in case n is large by using the central limit theorem.
00:40
So we are going to use this formula here, which is given by the p hat.
00:45
P hat is the proportion in the sample.
00:48
Z is the z score in that table, which depends on the confidence level of our interval, and the standard deviations given by this part here.
01:01
First, let's talk about the confidence interval for the mean.
01:05
So suppose that we have a sample mean of 10, a standard deviation in the population, 5, and our initial sample size of 100.
01:15
We just need to substitute these values in the formula above for the confidence interval for the mean.
01:22
And we can do that because n is large.
01:26
N is larger than 30 observations.
01:28
So we can use that formula for the sample to calculate the confidence interval for the mean.
01:34
We're going to get this results here.
01:40
And by just calculating this, you're going to get this confidence interval for the mean when we have a confidence level of 90%, 95 and 99, is given by this, which this part here represents the margin of error.
02:02
Now, if you increase the sample size, let's say to these two options here, what is going to happen with the margin of error? so for each one of these confidence intervals here, we can use the same formula, but now we just need to change the sample size.
02:21
So we are changing the simple size here...