The margin of error formula is
Assume that I created a 95% confidence interval for the mean hours studied for a test based on a sample of 100 students. The lower bound of this interval was 6 and the upper bound was 10. Assume that when I created this interval I knew the population standard deviation.
Calculate and report the population standard deviation.
I knew I use the E = zα/2 * (2√ n) formula (margin of error) but I know how to apply it to this problem. I also found that the sample mean is 8. Im just stuck on how to find the population standard deviation.
The margin of error E is the difference between the sample mean and the upper limit, or the sample mean and the lower limit.
For a 95% confidence interval the significance level is 0.05 (the amount of the population not in the confidence interval)
. is the point in the normal distribution that has 2.5% of the population below it, that point is -1.96
. is the point with 97.5% of the population below it, that point is 1.96.
So it doesn't really matter, all that changes is the sign