 # Very quick Q about confidence intervals

Which is correct? For the 95% confidence interval: x (mean) ± 1.96(stddev) or x (mean) ± 1.96(std error) i thought it was the second way, but a question on mock 1 had it so that the answer was calcualted the first way

If the population std dev is given, use the 1st one. If only the sample std dev is given used the second.

^No In truth it should only be the latter (the one with standard error), but strange things show up on CFA exams. The deal is that if you are estimating an average of a population, then use the std. error one, e.g., “Find a confidence interval for the average amount of money spent by a walmart shopper…”. Key word is “average”. The first interval is if you are estimating bounds on an individual observation from a normal population. E.g., “It is known that Walmart shoppers spend an amount of money normally distributed with mean \$90 and std. dev. \$40. Find a 95% C.I. for the amount of money spent by an individual WalMart shopper”. Note that here we are not doing any sampling and we are interested in an interval for an individual, not an average.

Yup, I mixed that up! Population mean has to be known to use the 1st one…

When referring to type 1 and type 2 errors, CFAI text says: The only way to avoid the trade off between the two types of errors is to increase the sample size. but doesnt increasing the sample size have the same effect as increasing the significance level? say u have: x (mean) ± 1.96(std error) if you increase the significance level, you have: x (mean) ± 1.658(std error) - THIS DECREASES THE CONFIDENCE INTERVAL if you increase the sample size, you have: x (mean) ± 1.96(a lower std error) - THIS DECREASES THE CONFIDENCE INTERVAL so both seem to have the same effect on the confidence interval.

If you’re increasing the significance level, you’re decreasing the probability of not rejecting a fallse null, but you’re also increasing the probability of rejecting a true null. That’s the tradeoff between Type I and Type II. The only way to solve the problem is to increase the sample size. I probably confused you even more, but that’s the only way I know how to explain it.

bpdulog Wrote: ------------------------------------------------------- > If you’re increasing the significance level, > you’re decreasing the probability of not rejecting > a fallse null, but you’re also increasing the > probability of rejecting a true null. That’s the > tradeoff between Type I and Type II. The only way > to solve the problem is to increase the sample > size. I probably confused you even more, but > that’s the only way I know how to explain it. This point is not sticking with me. I grasp almost all the information in the Level 1 curriculum, but this for the life of me is not intuitive.

bpdulog Wrote: ------------------------------------------------------- > If you’re increasing the significance level, > you’re decreasing the probability of not rejecting > a fallse null, but you’re also increasing the > probability of rejecting a true null. That’s the > tradeoff between Type I and Type II. The only way > to solve the problem is to increase the sample > size. I probably confused you even more, but > that’s the only way I know how to explain it. I understand every word you said. My only point was, if you look at the increase in signifance level vs. the increas in sample size mathematically, they look like they have the same effect

the show NY Wrote: ------------------------------------------------------- > bpdulog Wrote: > -------------------------------------------------- > ----- > > If you’re increasing the significance level, > > you’re decreasing the probability of not > rejecting > > a fallse null, but you’re also increasing the > > probability of rejecting a true null. That’s > the > > tradeoff between Type I and Type II. The only > way > > to solve the problem is to increase the sample > > size. I probably confused you even more, but > > that’s the only way I know how to explain it. > > > I understand every word you said. My only point > was, if you look at the increase in signifance > level vs. the increas in sample size > mathematically, they look like they have the same > effect I just took another look at your example, I see what you’re saying. Anyone have an answer?

Increasing the sample size reduces both P(Type I) and P(Type II). Increasing significance level increases P(Type II) while decreasing P(Type I).

Still don’t get the first part but by now, I’ve spent so much time on this, that it’s been tattooed on my brain haha. So will just recall the fact from memory if it’s on the exam