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Calculating a confidence interval

A confidence interval is often used to estimate the value of a population mean or the difference in means between two populations after a single sample has been collected. For example, for a population mean, we would want to know the 95% confidence interval for the population mean, otherwise we do not know the value of the population mean, and thus, cannot make any conclusions. For the difference in means, we would want to know the 95% confidence interval for the difference in means.If you’re just beginning statistics, you’ll probably be finding confidence intervals using the normal distribution (see #3 below). But in reality, most confidence intervals are found using the t-distribution (especially if you are working with small samples). Watch the video for an example:

A confidence interval is how much uncertainty there is with any particular statistic. Confidence intervals are often used with a margin of error. It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to survey the entire population. Confidence intervals are intrinsically connected to confidence levels.Confidence levels are expressed as a percentage (for example, a 95% confidence level).

It means that should you repeat an experiment or survey over and over again, 95 percent of the time your results will match the results you get from a population (in other words, your statistics would be sound!). Confidence intervals are your results and they are usually numbers. For example, you survey a group of pet owners to see how many cans of dog food they purchase a year. You test your statistic at the 99 percent confidence level and get a confidence interval of (200,300). That means you think they buy between 200 and 300 cans a year. You’re super confident (99% is a very high level!) that your results are sound, statistically. (Source: www.statisticshowto.com)

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“.

The U.S. Census Bureau routinely uses confidence levels of 90% in their surveys. One survey of the number of people in poverty in 1995 stated a confidence level of 90% for the statistics “The number of people in poverty in the United States is 35,534,124 to 37,315,094.” That means if the Census Bureau repeated the survey using the same techniques, 90 percent of the time the results would fall between 35,534,124 and 37,315,094 people in poverty. The stated figure (35,534,124 to 37,315,094) is the confidence interval. (Source: www.statisticshowto.com)