What confidence intervals express and what they don’t express If we would wish to be 99% confident the interval could widen to for example 36-44. Let’s take the example from above with a 95% confidence interval of 115 to 125. The more “secure”, or confident, we wish to be, the wider the interval: For population proportions we can calculate the population standard deviation (σ) and therefore we apply z-statistics. For population means we usually apply t-statistics as we calculate with the sample standard deviation (s). We can calculate confidence intervals for population means and confidence intervals for population proportion. This means that we can be 95% confident that the population mean ( µ ) is somewhere between 115 and 125. Say we do a 95% confidence interval for a sample mean (x̄) of 120 and that we calculate a confidence interval of 115 to 125. A confidence interval is a range of values within which we are confident, to a certain degree, that the population parameter is expected to fall, based on our sample results.
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