# Confidence Interval

A 95 percent confidence interval for the mean number of monthly customer visits to a grocery store is 28,000 to 32,000 customers. Which of the following is an appropriate interpretation of this confidence interval? A) If we repeatedly sample the population and construct 95 percent confidence intervals, 95 percent of the resulting confidence intervals will include the population mean. B) There is a 95 percent chance that next month the grocery store will have between 28,000 and 32,000 customer visits. C) We are 95 percent confident that if a sample of monthly customer visits is taken, the sample mean will fall between 28,000 and 32,000. D) If we repeatedly sample the population and compute the mean each time, 95 percent of the resulting sample means will be between 28,000 and 32,000. Thanks S

A) is true B) You would need to use a prediction interval for this. A C.I. is an estimator for a parameter. This is a prediction for an observation. C) Close. This would be a prediction interval for X-bar not a C.I. D) Same as C) but from a different perspective.

C?

map1 Wrote: ------------------------------------------------------- > C? No “This would be a prediction interval for X-bar not a C.I.”

Yeap, Joey is right, AGAIN!

Amazing how that Stats Ph.D. and 10 years of teaching stats in college pays off in answering CFA stats questions, huh?

Yeap!

Where is this question from? It seems poorly worded and the answer is almost just the definition of a CI. Just asking - will questions worded like this be on the exam?

You’re right - it’s an awful question because all that stuff aboutgrocery store, customers, 28000, etc. doesn’t affect the answer. They would never put a question on the exam that was so misleading.

Kind of really weird but I guess Prediction Interval interpretation of CI is OK? here is the answer. Q is from Schweser Qbank There are two interpretations of this confidence interval: a probabilistic and a practical interpretation. Probabilistic interpretation: We can interpret this confidence interval to mean that if we sample the population of customers 100 times, we can expect that 95 (95%) of the resulting 100 confidence intervals will include the population mean. Practical interpretation: We can also interpret this confidence interval by saying that we are 95% confident that the population mean number of monthly customer visits is between 28,000 and 32,000. can somebody elablorate/clarify? S

No. Read it more carefully - these are subtle. Answer C) is: "We are 95 percent confident that if a sample of monthly customer visits is taken, the sample mean will fall between 28,000 and 32,000. " Schweser Practical interpretation: "We can also interpret this confidence interval by saying that we are 95% confident that the population mean number of monthly customer visits is between 28,000 and 32,000. " The former is about the sample mean (prediction interval); the latter is about the population mean (confidence interval).

The probabilistic interpretation is the definition of the confidence interval. Now, what is the difference between their practical interpretation and the answer included in C?

Eagle Joey:))

I would actually say both are probabilistic definitions. The one you like better I would call the “frequentist” definition and the practical one I would call the “Bayesian” definition. C) is talking about a sample mean - the number you actually calculate after sampling. The practical interpretation is talking about the unknown and unknowable population mean that is being estimated by the sample mean.

map1 Wrote: ------------------------------------------------------- > Eagle Joey:)) ? I was an Eagle Scout once…trustworthy, loyal, helpful, friendly, courteous, and all that.

JoeyDVivre Wrote: ------------------------------------------------------- > Amazing how that Stats Ph.D. and 10 years of > teaching stats in college pays off in answering > CFA stats questions, huh? JoeyDVivre just an off topicquestion , did u lecture at Lafayette College in Easton ??

Yep

wow ! guys like you giving free advices to newbies like us Congrats & many thanks for ur time Best Regards

Yes, you are very privileged as are all the people I’ve taught. Even the ones who slashed my tires. Twice.