However, it is more rational to assume that the one confidence interval that you took is one of the 95% that capture the population mean than to assume it doesn't. As to the specific confidence interval that you did construct, the probability that the true population mean falls within the interval is either 1 or 0: either the interval captures the mean or it doesn't.
As you'll see, you construct your confidence interval in such a way that if you took many more means and put confidence intervals around them, 95% of the confidence intervals would capture the true population mean. Just as there are many possible samples that you might have taken, but didn't, there are many possible confidence intervals you might have constructed around the sample means, but couldn't. No, it doesn't, although it might well be. (And here you can see the relationship to "plus or minus 3 percentage points.") Does that tell you that the true population mean is somewhere between 45 and 55? Perhaps the interval extends from 45 to 55. You do so by constructing a confidence interval around that mean of 50 mg/dl. You can make use of the sample standard deviation and the number of HDL values that you tabulated in order to get a sense of how much play there is in that sample estimate.
Although the value of 20 that you calculate for the sample standard deviation is a statistic, it is the same as the known population standard deviation of 20. Over many repeated samples, the grand mean-that is, the mean of the sample means-would turn out to be very, very close to the population parameter.īut your resources don't extend that far and you're going to have to make do with just the one statistic, the 50 mg/dl that you calculated for your sample. You're aware that the mean is a statistic, not a population parameter, and that another sample of 100 adults, on the same diet, would very likely return a different mean value. Suppose that you measured the HDL level in the blood of 100 adults on a special diet and calculated a mean of 50 mg/dl with a standard deviation of 20. Don't let that get you thinking that you can use confidence intervals with normal distributions only. But it's easiest to understand what they're about in symmetric distributions, so the topic is introduced here.
NORMAL DISTRIBUTION PERCENTAGES WORKSHEET PLUS
The most familiar use of a confidence interval is likely the "margin of error" reported in news stories about polls: "The margin of error is plus or minus 3 percentage points." But confidence intervals are useful in contexts that go well beyond that simple situation.Ĭonfidence intervals can be used with distributions that aren't normal-that are highly skewed or in some other way non-normal. Learn More Buy Confidence Intervals and the Normal DistributionĪ confidence interval is a range of values that gives the user a sense of how precisely a statistic estimates a parameter. Statistical Analysis: Microsoft Excel 2010
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