A post explains "Confidence Intervals" in several real life examples. I guess I partly understand the main idea in it and have some

I guess I clearly understand the example of the U.S. Census Bureau in that post, which routinely uses confidence levels of 90% in their surveys.

"the number of people in poverty in the United States is 35,534,124 to 37,315,094" means (35,534,124 to 37,315,094) is the confidence interval.

Assume the Bureau repeats the survey 1,000 times, the confidence levels of 90% means that the stated number is between (35,534,124 to 37,315,094) at least 900 times. Maybe 36,000,000 is people in poverty, maybe less a bit, maybe greater a bit, any number in the interval is as expected.

So far so good.

I don't really understand the part in the example of "2008 Gallup survey"

For the European data, one can say with 95% confidence that the true population for wellbeing among those without TVs is between 4.88 and 5.26.

It does not make sense to say there 4.88 people don't have TV in their home.

what does the confidence interval “between 4.88 and 5.26“ mean there?


I went to read the post, and I also found it a bit unclear

A 2008 Gallup survey found that TV ownership may be good for wellbeing. The results from the poll stated that the confidence level was 95% +/-3, which means that if Gallup repeated the poll over and over, using the same techniques, 95% of the time the results would fall within the published results. The 95% is the confidence level and the +/-3 is called a margin of error. At the beginning of the article you’ll see statistics (and bar graphs). At the bottom of the article you’ll see the confidence intervals. For example, “For the European data, one can say with 95% confidence that the true population for wellbeing among those without TVs is between 4.88 and 5.26.” The confidence interval here is “between 4.88 and 5.26“.

I had to go read the original Gallup survey results. There it is indicated that respondents were asked to indicate their own well being on a scale from 0 to 10, where 10 represents "the best possible life for you" and 0 the worst. So $[4.88, 5.26]$ is the 95% confidence interval around the score reported by people without the TV.

The confidence interval seems to be calculated from a frequentist perspective, meaning that as you correctly state in your question, it refers to the data generating process (the survey). It indicates that "if the survey were to be repeated a large number of times, each time by randomly sampling the same number of individuals from the population, the average well being rating for people without a TV is expected to fall within the confidence interval 95% of the times".

  • $\begingroup$ Thanks for your comprehensive explanation. Is my understanding about the example of the U.S. Census Bureau right? $\endgroup$ – WXJ96163 Apr 7 '20 at 11:45
  • $\begingroup$ Yes, it is correct. $\endgroup$ – matteo Apr 7 '20 at 12:32

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