Question

Any ideas? (Multiple Choice)

Which of the following statements is true about the 95% confidence interval of the average of a sample?

A) 95 of 100 avgs of samples will be within the limits of the confidence interval.

B) There is a 95% chance the avg of the population to be within the limits of this confidence interval.

C) There is a probability of 5% the avg of the population to be within the limits of this confidence interval.

D) If we repeated the survey 100 times, in 95 of them the avg would be within the limits of this confidence interval.

Answer 1

I believe the correct answer is D (because it says for one sample). Do you agree? maybe is B I am not sure but I am more sure for D..

Answer 2

@kropot72 Is the statistician here. He'll help you out ;]

Answer 3

The confidence interval relates to setting limits between which the population average lies. Choice D does not mention the population average. The correct choice is B.

Answer 4

@kropot72 If you don't mind and if you have the time, do you mind explaining confidence intervals to me with an example? Like I said, if you have the time/are willing to, otherwiseit's ok =]

Answer 5

Looks like this will be big lol.

Answer 6

CONFIDENCE INTERVALS FOR POPULATION MEANS
For reasons of time, cost, feasibility, and so on, it is often not practical to measure all members of a population and calculate the population mean. In such cases it is usual to make a Point Estimate of the population mean by calculating the mean (x-bar) of a random sample selected from this population. The sample mean is then used to estimate the mean of a population.
Using Sample Statistics to make estimates of Population Parameters is called Statistical Inference.
Sample means vary from sample to sample, so it is important to have some indication of the accuracy of the estimate. Confidence Intervals are a measure of the accuracy of these estimates.
A p% Confidence Interval for the population mean is an interval such that on average, p out of every 100 such intervals will contain the population mean.
If ther mean from a sample of size n from a Normally distributed population is x-bar, it can be shown that in 95% of all cases, the population mean mu lies in the interval
\[\bar{x}-1.96\frac{\sigma}{\sqrt{n}}< \mu <\bar{x}+1.96\frac{\sigma}{\sqrt{n}}\]
where sigma is the population standard deviation.

Answer 7

If the mean....*

Answer 8

@kropot72 sigma is the standard deviation then what is the "if the mean...*" for?

Answer 9

"If the mean....*" is a correction for a typo in my posting about CONFIDENCE INTERVALS FOR POPULATION MEANS.

Answer 10

I originally posted "If ther mean from a sample of size n........"

Answer 11

@kropot72 and genius12. Thank you a lot both of you. Kropot72 are you absolutely sure? At first I was thinking about B but later i decided that the correct one is D because it seays about one sample. I also read this in wikipedia:

For users of frequentist methods, various interpretations of a confidence interval can be given.
The confidence interval can be expressed in terms of samples (or repeated samples): "Were this procedure to be repeated on multiple samples, the calculated confidence interval (which would differ for each sample) would encompass the true population parameter 90% of the time."[1] Note that this does not refer to repeated measurement of the same sample, but repeated sampling.[2]
The explanation of a confidence interval can amount to something like: "The confidence interval represents values for the population parameter for which the difference between the parameter and the observed estimate is not statistically significant at the 10% level".[5] In fact, this relates to one particular way in which a confidence interval may be constructed.
The probability associated with a confidence interval may also be considered from a pre-experiment point of view, in the same context in which arguments for the random allocation of treatments to study items are made. Here the experimenter sets out the way in which they intend to calculate a confidence interval and know, before they do the actual experiment, that the interval they will end up calculating has a certain chance of covering the true but unknown value.[3] This is very similar to the "repeated sample" interpretation above, except that it avoids relying on considering hypothetical repeats of a sampling procedure that may not be repeatable in any meaningful sense. See Neyman construction.
In each of the above, the following applies: If the true value of the parameter lies outside the 90% confidence interval once it has been calculated, then an event has occurred which had a probability of 10% (or less) of happening by chance.

Answer 12

@Social I'm sticking with B for the reason that I gave.

Answer 13

@kropot72 I just asked because I believe that D is also correct. thank you a lot. Can you help me and with the other one pleasE?

Answer 14

You're welcome :)
Please post the other one as a new question. Thanks.

Answer 15

@kropot72 I already posted it and I mentioned you before.. I will do it again..

Answer 16

@kropot72 maybe B is wrong. look what I found.

We will now look at a series of different mistakes that can be made when dealing with confidence intervals. One incorrect statement that is often made about a confidence interval at a 95% level of confidence is that there is a 95% chance that the confidence interval contains the true mean of the population.

http://statistics.about.com/od/Inferential-Statistics/a/Four-Confidence-Interval-Mistakes.htm

Answer 17

Based on the following strict definition of a confidence interval it could be argued that none of the choices is correct:
A 95% confidence interval is the interval produced in such a way that if a large number of small samples (size < 30) are taken, and a 95% confidence interval for the population mean is worked out from each sample, then 95% of the confidence intervals will include the true population mean; the other 5% will not.

The question does not state the sample size, the probability distribution of the underlying population, or the standard deviation of the underlying population.Therefore it is not really possible to make any definite statement about the meaning of the confidence interval.

Answer 18

@kropot72 so? what do you suggest? Everything is false?

Answer 19

After reflection I would now say all the choices are false. It has been an interesting question!

Answer 20

@kropot72 Thank you for trying. Are you sure? Why do you reject all the choices? Can you tell me the justification please? (not to test you but to learn)...

Answer 21

May I answer you with a question? Given the following definition
"A p% Confidence Interval for the population mean is an interval such that on average, p out of every 100 such intervals will contain the population mean."
do you think that any of the choices are correct?

Answer 22

@kropot72 Yes of course.. But i dont understand why to ask such a question with everything false.. Imagine that i am looking some days to find an answer and is not so easy.. Why not to be?? I still be confused!

Answer 23

Note that the question is "about the 95% confidence interval of the average of a sample". A Confidence Interval is for the population mean, and does not relate to the average of one sample.
Choice B comes closest to being correct, however the lack of detail about the method used to calculate the confidence interval (for example: Is the standard deviation of the underlying population known, or is it estimated from a single sample?) makes it uncertain.

Answer 24

I might add that the question is poorly constructed :(

Answer 25

@kropot72 this is the most difficult part of these wuestions. Believe me i am breaking my mind every time I have to answer them and I study all the internet sources before answering... However here I must choose one answer so I have to choose between B and D. A and C are definitely wrong. You still supporting B and not D?

Answer 26

I also found this in a book: "when you see or use a 95% confidence interval, remember that if you had chosen 100 different samples and have calculated their average and the confidence interval, in 95 of these cases the intervals would contain the value of the average of the population".

This is why i was thinking about D.

Answer 27

ohh.. wait.. It says for different samples. The D option i think that means for the same sample, because it says for the repetition of the research and the research says about one sample..

Answer 28

@Social Option D states "in 95 of them the avg would be within the limits of this confidence interval". This option does not state the 'population average', therefore it is not correct.

Answer 29

@kropot72 Yes you are correct. Finally is B. When I will check the answers I will tell you.. The most difficult part is the Meaning and interpretation!

Thank you again

Answer 30

You're welcome :)