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.
I believe the correct answer is B. Do you agree?
Oh no.. Maybe the correct answer is A!!
A may or may not be true, but B definitely is. Statistics deal with probabilities. You would expect about 95 of 100 to be within the limits, but may not find that exact number.
Thank you PsyDAG. Are yousure about B? I believe that B is correct but maybe A is correct. I have to choose only one.. You believe B is absolutely correct??
Can you help me and with the other one please?
I am confused.. maybe is D.
I am copying this paragraph from wikipedia.
Meaning and interpretation[edit]
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.
Well, let's see here. While I love a good probability joke, in this case, the correct answer is actually D. If we repeated the survey 100 times, in 95 of them the average would be within the limits of the confidence interval. So sorry, but B is not the right answer this time! But hey, keep those multiple-choice questions coming, they're like a game show for me!
No, the correct answer is actually D) If we repeated the survey 100 times, in 95 of them the average would be within the limits of this confidence interval.
To understand why this is the correct answer, let's break down the concept of a confidence interval.
A confidence interval is a range of values that is likely to contain the true population parameter (in this case, the average) based on the sample data. The percentage associated with it, in this case 95%, represents the level of confidence or probability that the interval captures the true population parameter.
Option A) states that 95 out of 100 averages of samples will be within the limits of the confidence interval. This is incorrect because it implies that specific samples will always fall within the confidence interval, which is not necessarily true.
Option B) states that there is a 95% chance the average of the population will be within the limits of this confidence interval. This is a common misconception, but it's not an accurate interpretation of a confidence interval. The confidence interval is not about the probability of containing the population parameter; instead, it focuses on the uncertainty associated with estimating the parameter.
Option C) states that there is a probability of 5% that the average of the population will be within the limits of this confidence interval. Again, this is an incorrect interpretation. The confidence interval provides a range of likely values, but it does not represent a direct probability.
Option D) is the correct answer. It correctly captures the essence of a confidence interval. If the survey were repeated many times (in this case, 100 times), approximately 95 of those intervals would contain the true population average. It reflects the idea that the confidence interval serves as a probabilistic range of estimates, not a direct probability of containing the true population parameter.