00:02
Out of 200 observations, 30 observations said that they work at home at least once per week.
00:10
So this means that the proportion in the sample of people that work at least once per week at home is equal to 30 divided by the sample, which is 0 .15.
00:27
Now, to compute a 99 % confidence interval for the population proportion, we need to use the following formula, which is the sample proportion plus and minus the z score, multiplied by the square root of the sample standard deviation, which is given by this.
00:55
We can use the normal distribution here because the sample size is large.
01:04
And this means that we can approximate the distribution of the sample proportion to be normal with the mean equals to the population proportion and i standard deviation equals to the square root of this.
01:26
So now i just need to find what is this z score.
01:32
The z score for a 99 % confidence interval is equals to 2 .576.
01:40
And we can find this value using the z table, which is the z in this standard normal distribution, with an area left to it equals to 0 .995.
01:57
Now, i just need to plug in all the values that we know from the question to find the confidence interval that we want...