Interpretaton of confidence interval. I have read two books that explicitly state that the (1-alpha)% confidence interval should be interpreted as: If you construct 100 such confidence intervals, alpha of them are expected to not contain the true population statistic and (1-alpha) of them are expected to contain the true population statistic.

mangicele4s 2022-09-20 Answered
Interpretaton of confidence interval
I have read two books that explicitly state that the ( 1 α )% confidence interval should be interpreted as:
If you construct 100 such confidence intervals, α of them are expected to not contain the true population statistic and ( 1 α ) of them are expected to contain the true population statistic.
and not as
There is a ( 1 α ) probability that the true population statistic is contained in the confidence interval.
In my view, they both equivalent: If you make the first statement, you implicitly make the second statement. You are looking at any one arbitrary confidence interval, which in itself is a random variable, the generic confidence interval should, therefore, be subject to the second statement. Do things change when this random variable is actually realized?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Triston Donaldson
Answered 2022-09-21 Author has 10 answers
Step 1
I think confidence intervals are better understood in the following way. There is an infinite set of constant open intervals. Some of them cover the population statistic θ and some of them don't.
Step 2
Now the (random) confidence interval is just a mechanism to draw an interval from this set. So the ( 1 α ) % is the chance of picking a constant interval that covers θ. But whatever interval is drawn (or realized), since each of these interval is constant, the probability that it contains θ can only be 0 or 1.
Did you like this example?
Subscribe for all access
batejavizb
Answered 2022-09-22 Author has 4 answers
Step 1
(as background context a 95% confidence interval of the number of voters voting for a particular party was found to be [36%,44%]):
Step 2
For example, in the poll example outlined in the introduction, to be 95% confident that the actual number of voters intending to vote for the party in question is between 36% to 44%, should not be interpreted in the common-sense interpretation that there is a 95% probability that the actual number of voters intending to vote for the party in question is between 36% to 44%. This would be technically incorrect. The actual meaning of confidence levels and confidence intervals is rather more subtle. In the above case, a correct interpretation would be as follows: If the polling were repeated a large number of times (you could produce a 95% confidence interval for your polling confidence interval), each time generating about a 95% confidence interval from the poll sample, then approximately 95% of the generated intervals would contain the true percentage of voters who intend to vote for the given party. Each time the polling is repeated, a different confidence interval is produced; hence, it is not possible to make absolute statements about probabilities for any one given interval.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-08-12

Anna flipped a coin to choose either her right hand or her left hand, and also she asked the therapists to identify the named hand by placing their hand just under Anna's hand without seeing it and without touching it. Among 358 trials, the touch therapists were correct 172 times. Complete parts​ (a) through​ (d).
a) Given that Anna used a coin toss to elect either her right hand or her left hand, what proportion of correct responses would be anticipated if the touch therapists made arbitrary suppositions?( Type an integer or a numeric. Do not round.)
b) Using Anna's sample results, what's the stylish point estimate of the therapists' success rate?( Round to three decimal places as demanded.)
c) Using Anna's sample results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.
Round to three decimal places as demanded-?<p<?

asked 2021-01-10

The average zinc concentration recovered from a sample of measurements taken in 36 different locations in a river is found to be 2.6 grams per liter. Find the 95% confidence intervals for the mean zinc concentration in the river. Assume that the population standard deviation is 0.3 gram per liter. (Z0.025=1.96,Z0.005=2.575)

asked 2021-02-23
Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let j: denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence intervals (7-8, 9.6)
(a) Would 2 90%% confidence interval calculated from this same sample have been narrower or wider than the glven interval? Explain your reasoning.
(b) Consider the following statement: There is 9 95% chance that Is between 7.8 and 9.6. Is this statement correct? Why or why not?
(c) Consider the following statement: We can be highly confident that 95% of al bottles ofthis type of cough syrup have an alcohol content that is between 7.8 and 9.6. Is this statement correct? Why or why not?
asked 2021-08-04

The average annual mileage of a car is 23,500 kilometers, with a standard deviation of 3900 kilometers, according to a sample of 100 Virginians who own cars.
Assume that the measurement distribution is roughly normal.
a) Create a 99 percent confidence interval for the typical Virginian vehicle's annual mileage in kilometers.
b) If we assume that Virginians drive an average of 23,500 kilometers per year, what can we say with 99 percent certainty about the potential extent of our error?

asked 2022-03-24
Let's say I have two samples of results of two bernoulli experiments.
H0:p1=p2
H1:p1p2
And I want to try to reject H0 at a confidence level.
I already know a proper way to solve this, but I was wondering, if I have a confidence interval for p1 and p2, at the same level of significance. Can I just check if the intervals overlaps each other to test this?
asked 2021-09-18

In a survey of 2695 adults, 1446 say they have started paying bills electronically in the last year.
Construct a 99% confidence interval for the population proportion. 
Interpret your results. Choose the correct answer below. 
A) With 95% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval 
B) With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval. 
C) The endpoints of the given confidence interval show that adults pay bills online 99% of the time.

asked 2022-03-26
Confidence interval and standard deviation
I'm currently talking an intermediate course in finance where we want to calculate Value-at-Risk for portfolios and bonds. To use this VaR formula I need to know the standard deviation for different confidence intervals. Now my teacher have put up the following standard deviation for different confidence intervals:
C.I90=+1,64S.d
C.I95=+1,96S.d
C.I98=+2,33S.d
C.I99,9=+3,09S.d
When I watched an old exam for calculating VaR, the C.I was 99% and the student wrote that the S.d was equal to 2,33. How is this possible? (P:s the student got an A on this exam).

New questions