# Calculate a confidence interval?

Can someone explain to me what it would mean to “calculate” a confidence interval? I know that 68%, 90%, 95%, 99% fall within 1, 1.65, 1.96, and 2.58 SD, but what does it mean to calculate it?

mean +/- (1.96 ect.)*st. dev/sq rt. of n

we never resolved this the other day… when do you use std dev and when do you use standard error

I believe you just use SD when that’s all your given. I remember a question like this on the mock or sample. Otherwise if give ‘n’ always use the standard error. Just my take anyways…

st.dev/sq rt of n is the error and that’s what you used estimating from a sample. if you have entire population then you use st dev since you can’t have sample error (there is no sample).

cfa=no life, thanks! makes perfect sense.

Thanks all. I got it, it’s just kind of all running together. I feel like I will pass in December if will be able to pass in June. I’m really getting in, just piece by piece. I’ve honestly put in well over 300 hours, but I can say, I wish i put in a lot more, and I have a degree in Finance.

CFA=NOLIFE Wrote: ------------------------------------------------------- > st.dev/sq rt of n is the error and that’s what > you used estimating from a sample. > > if you have entire population then you use st dev > since you can’t have sample error (there is no > sample). Sorry, can anyone confirm this? I am looking at Schweser answer solutions that dont seem to always follow this rule. Can anyone please help. I’ve spent a long time trying to figure this out. It has nothing to do with sample/population size, right? And then I see this language below, which i can’t figure out. Thanks in advance! Schweser Question ID 22958: A sample of 100 recently hired employees shows an average starting salary of \$50,000 and a standard deviation of \$3,000. Assuming the population has a normal distribution, construct a 90% confidence interval for the starting salary of a recently hired employee. Answer: 90% confidence interval is X ± 1.65s = 50,000 ± 1.65(3,000) = \$45,050 to \$54,950. Note that this is a confidence interval for a single observation, which we estimate as a number of standard deviations from the mean. If we were constructing a confidence interval for the population mean, we would need to use the standard error (3,000 / sq rt of 100). Schweser Question ID 1770: Question: A traffic engineer is trying to measure the effects of carpool-only lanes on the expressway. Based on a sample of 20 cars at rush hour, he finds that the mean number of occupants per car is 2.5, with a standard deviation of 0.4. If the population is normally distributed, what is the confidence interval at the 5% significance level for the number of occupants per car? Solution: We can use standard distribution tables because the sample is so large. From a table of area under a normally distributed curve, the z value corresponding to a 95%, one-tail test is: 1.65. (We use a one-tailed test because we are not concerned with passengers arriving too early, only arriving too late.) Here, we do not divide by the standard error, because we are interested in a point estimate of making our flight. The answer is one hour, twenty minutes + 1.65(30 minutes) = 2 hours, 10 minutes.

CFA=NOLIFE Wrote: ------------------------------------------------------- > st.dev/sq rt of n is the error and that’s what > you used estimating from a sample. > > if you have entire population then you use st dev > since you can’t have sample error (there is no > sample). this is very helpful. I was confused about this as well. thanks a bunch.

no no no! 1) constructing a CI is when you use the 1.96 numbers and such to come up with a low/hi range that is 95% likely or so to contain a value. 2) whether you use SD, or SD/sqrt(N) (called the standard error of the mean) depends on what kind of value you want the CI to contain. If you are trying to estimate the population mean by using the sample mean’s value, use the standard error. If you are trying to find the likelihood that an individual member of a sample or population is within a given range of the mean, use the standard deviation.

So use only Std. deviation always when asked to calculate CI?

see above…it depends…i guess a safe bet is if you are given population use st. error.

More often you will be using the standard error to find out how close your sample mean is to the population mean. You will construct a CI using the sample’s mean and standard error to create a CI that contains the population’s mean with X% confidence.