# Confidence interval width

I've been asked a few questions in regards to confidence interval width estimates and cant seem to find the answer on a practice quiz i'm doing.

You have a sample with sample mean x̄=100 and sample standard deviation s=10 . The distribution of the sample means of the bootstrap samples is bell-shaped with the standard error SE=2 . What is the width of a 95% confidence interval for the population mean?

I calculated a 95% confidence interval with x̄ ± 2 ⋅ SE = 4 and then multiplied that by 2 to get the width of the confidence interval which was equal to 8. however the answer is wrong and after going through my notes I cant find where I have gone wrong.

• were there options to choose from? Apr 30, 2019 at 1:54
• your answer looks correct, because 95% confidence = 1.96 standard deviations in either direction. Apr 30, 2019 at 1:54
• is 7.84 an answer choice? Apr 30, 2019 at 1:55
• it wasn't multiple choice question but 8 is considered incorrect, I will try 7.84 next time the question pops up Apr 30, 2019 at 2:02

Your sample size is $$n=25$$ because, $$s/SE= 5 = \sqrt{n}$$. Thus, the variance of the population is $$n/(n-1)s^2 = 10.42^2$$. Hence the SD of the distribution of the mean is $$10.42/5 = 2.08$$ and the $$95\%$$ conf. int. for the population mean is approximately $$4 \times 2.08 = 8.32$$.