One confusion on confidence interval here… if the question said, ‘construct a 95% C.I. for mean=0 and s.d.=4’ I would do this two different ways. 1. 95% is 1.96s.d.'s in each direction… so I would add (1.96*4) to the mean, and subtract it. leaving me 95% C.I. of -7.84 to 7.84 or 2. use the stander error formula and get - - - - mean +/- 1.96*(var/n) which one would be appropriate to use in which situation?
use st error is sample is < 30 ??? CI = mean +/- 1.96 (st dev) or CI = mean +/- 1.96 (st dev/sq root of N)
If you’re estimating a population parameter, then the variance of the sampling distribution (the distribution of the sample means) is equal to variance divided by the sample size. Standard deviation becomes standard error, which equals the standard deviation divided by the square root of n. This comes in play when we build confidence intervals because we are trying to make inferences about the population parameter. Hence, the central limit theorem would apply and we’d use the standard error. If you’re looking at a sample distribution, we’re relying on descriptive statistics. So we’re merely describing the distribution of the sample. By definition, then when we say “95% of the values in the sample fall between which two points?”, we are using just the standard deviation, times 1.96. Not the standard error. Again, look at what the question is trying to accomplish. If it involves parametric inference (confidence intervals, hypothesis testing) you are using standard error. If you’re describing a sample (like a group of CFA test takers), then you just use standard deviation.
gdiddy Wrote: ------------------------------------------------------- > If you’re estimating a population parameter, then > the variance of the sampling distribution (the > distribution of the sample means) is equal to > variance divided by the sample size. Standard > deviation becomes standard error, which equals the > standard deviation divided by the square root of > n. This comes in play when we build confidence > intervals because we are trying to make inferences > about the population parameter. Hence, the > central limit theorem would apply and we’d use the > standard error. > > If you’re looking at a sample distribution, we’re > relying on descriptive statistics. So we’re > merely describing the distribution of the sample. > By definition, then when we say “95% of the values > in the sample fall between which two points?”, we > are using just the standard deviation, times 1.96. > Not the standard error. > > Again, look at what the question is trying to > accomplish. If it involves parametric inference > (confidence intervals, hypothesis testing) you are > using standard error. If you’re describing a > sample (like a group of CFA test takers), then you > just use standard deviation. THANX, THAT HELPS SO POPULATION —> ST ERROR FOR CONF INTERVAL ----> USE N I N DENOM IF SEEKING VAR SAMPLE – USE ST DEV TO GET CONF INTERVAL, USE N - 1 TO GET VARIANCE OF SAMPLE WONT FORGET IT NOW!
nice, thanks gdiddy