“We are 99% confident that the mean amount of time that all employees at this company think is wasted on meetings each week is between 10.2 and 14.6 hours.” If these conditions hold, we will use this formula for calculating the confidence interval: The sample size is greater than or equal to 30 and population standard deviation known OR Original population normal with the population standard deviation known. Setting the discussion above aside, the general rule for when to use a z-interval calculation is: As you can imagine, if we don’t know the population mean (that’s what we are trying to estimate), then how would we know the population standard deviation? When to use a z-interval What makes it strange? Well, in order to use a z-interval, we assume that \(\sigma\) (the population standard deviation) is known. Even so, it is common enough that we will talk about it here! This procedure is often used in textbooks as an introduction to the idea of confidence intervals, but is not really used in actual estimation in the real world.
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