Asked by Fakie
Give a correct interpretation of a 99% confidence level of 0.102 is less than p is less than 0.236 we are 99% confident that the interval from 0.102 to 0.236 actually does contain the true value of the population proportion p there is a 99% chance that the true value of p will fall between 0.102 and 0.236 99% of sample proportions fall between 0.102 and 0.2364 your confidence and 99% of values between 0.102 and 0.236 represent the true value of the population proportion p
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Correct concise interpretation
- We are 99% confident that the interval from 0.102 to 0.236, computed by this method from our sample, contains the true population proportion p.
What that means (frequentist view)
- If we repeated the same sampling and interval‑building process many times, about 99% of those intervals would contain the true p. The 99% describes the long‑run reliability of the method, not a probability assigned to p after the data are seen.
Common incorrect statements and why they are wrong
- "There is a 99% chance that the true value of p lies between 0.102 and 0.236." — Strictly incorrect in frequentist terms because p is a fixed (nonrandom) constant; the probability statement applies to the procedure, not to p after the data are observed. (Many texts still use the informal phrase "99% chance" but the long‑run interpretation above is more precise.)
- "99% of sample proportions fall between 0.102 and 0.236." — Wrong: the interval was computed from one sample; it does not describe the distribution of sample proportions.
- "99% of values between 0.102 and 0.236 represent the true value of p." — Nonsensical: there is only one true p, not multiple "true values" inside the interval.
Short recommended wording you can use
- "Using this sampling method, we are 99% confident that the interval [0.102, 0.236] contains the true population proportion p."
- We are 99% confident that the interval from 0.102 to 0.236, computed by this method from our sample, contains the true population proportion p.
What that means (frequentist view)
- If we repeated the same sampling and interval‑building process many times, about 99% of those intervals would contain the true p. The 99% describes the long‑run reliability of the method, not a probability assigned to p after the data are seen.
Common incorrect statements and why they are wrong
- "There is a 99% chance that the true value of p lies between 0.102 and 0.236." — Strictly incorrect in frequentist terms because p is a fixed (nonrandom) constant; the probability statement applies to the procedure, not to p after the data are observed. (Many texts still use the informal phrase "99% chance" but the long‑run interpretation above is more precise.)
- "99% of sample proportions fall between 0.102 and 0.236." — Wrong: the interval was computed from one sample; it does not describe the distribution of sample proportions.
- "99% of values between 0.102 and 0.236 represent the true value of p." — Nonsensical: there is only one true p, not multiple "true values" inside the interval.
Short recommended wording you can use
- "Using this sampling method, we are 99% confident that the interval [0.102, 0.236] contains the true population proportion p."
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