# Quants: Need help with Confidence Intervals

I just cant seem to decide whether to use the standard error or standard deviation. I’d be glad if someone could state me the reason behind this or just cite the CFAI book/Schweser notes page no. Thanks for the help. =================================================== A nursery sells trees of different types and heights. Suppose that 75 pine trees are sold for planting at City Hall. These 75 trees average 60 inches in height with a standard deviation of 16 inches. Using this information, construct a 95% confidence interval for the mean height of all trees in the nursery. A) 60 + 1.96(16). B) 0.8 + 1.96(16). C) 60 + 1.96(1.85). D) 0.8 + 1.96(1.85). Your answer: A was incorrect. The correct answer was C) 60 + 1.96(1.85). Because we know the population standard deviation, we use the z-statistic. A 95% confidence level is constructed by taking the population mean and adding and subtracting the product of the z-statistic reliability (zα/2) factor times the known standard deviation of the population divided by the square root of the sample size: x ± zα/2 × ( σ / n1/2) = 60 ± (1.96) × (16 / 751/2) = 60 ± (1.96) × (16 / 8.6603) = 60 ± (1.96) × (1.85).

If it says find a C.I. for the MEAN or AVERAGE use std. error. Otherwise use std. dev.

Oh, and I don’t see the standard deviation of the population - isn’t that the standard deviation of the sample? The sample is large, you can use z.

All 4 answers are wrong. As usual. I dislike these prep-providers.

CFAI volume 1, p.433-436

cfaisok Wrote: ------------------------------------------------------- > All 4 answers are wrong. > > As usual. I dislike these prep-providers. Why do you think all 4 answers are wrong?

Probably because of the minus sign missing.

Oh yeah…

Hi map: Missing minus [or you could substitute 1.96 by 1.65 using asymmetric intervalls starting at minus infinity]

I am not waiting for a minus. But it is obvious that the quality of many questions is questionable. The Prepproviders should: A) review Procedures by an internal quality reviewer B) Disclose the conflict C) Make additional compensation arrangement with CFAI D) use soft dollar arrangements to pay the trees

They should actually hire experts in the fields to check their stuff…

Joey, your replay sounds a bit like answer A. If you choose A, you will get one point and pass this exam with 100 %.

Hey Joey thanks so much for the help but my concepts are still a bit hazy it’d be great if i was helped a tad more on this HOW DO I SPOT a question wherein I’m supposed to use the foll ? CI = [mean or avg] +/- [test statistic]x[std deviation] Here’s another one where i went wrong Construct a 90% confidence interval for the starting salaries of 100 recently hired employees with average starting salaries of \$50,000 and a standard deviation of \$3,000 assuming the population has a normal distribution. A) 50,000 +/- 1.65(300). B) 30,000 +/- 1.65(5,000). C) 50,000 +/- 1.65(3,000). D) 50,000 +/- 1.65(30,000). Your answer: A was incorrect. The correct answer was C) 50,000 +/- 1.65(3,000). 90% confidence interval is X ± 1.65s = 50,000 ± 1.65(3,000) = \$45,050 to \$54,950. Should i conclude that… Use standard error for the TREES question cuz i’ve been asked CIs for the MEAN (or AVG) Use standard deviation for the SALARIES question cuz i’ve been asked CIs for the SALARIES And thanks to “map” , I’m going through the pages you cited, I’m reasonably clear on the first aspect (when to use the std error)

This second question is not asking you to build a confidence interval to determine with 90% certainty that the true mean falls in that interval (that is in 90% of the cases when you take a sample, calculate the mean of the sample, and calculate the interval, it will contain the true mean of the population). This is an improper use of the “confidence interval” term. The problem only asks to build a range around the sample mean, not one that would nclude the mean of the population in 90% of the cases.