But how did you get the standard error of the mean? You took the standard deviation of the population and divided it by the square root of the sample size. = σ Can you do that here? What problem do you run into? Well, to calculate the standard error of the mean you have to take the standard deviation of the population and divide it by the square root of N. But we don’t have We don’t have the standard deviation of σ. If we don’t have that we can’t calculate the standard error of the the population. σM, mean. If you don’t have you can’t calculate Z! If you can’t calculate Z, you can’t do σM a Z-test. Bummer. So what do you do! Clearly, we can’t do a Z-test. But that doesn’t mean we just have to give up. After all, we don’t have the standard deviation of the population, but we do have the next best thing. We’ve got an of the standard deviation of the population. We’ve got the estimate standard deviation of the If we take the standard deviation of the sample and sample. divide it by the square root of the sample size, we won’t get but we’ll have an σM estimate of The symbol for an estimate of the standard error of the mean is S. σM. = S Using the data provided above we get… = = = = .6 S Okay, so now we’ve got an of how far off, on average, sample means are going estimate to be off by when they’re trying to estimate that comparison value of 25. Now we can take our difference from the comparison value, 31 25 = 6, and divide it by the one – difference of sample means from this comparison value, 0.6. This will give us average an estimate of the number of standard deviations that our sample mean above the comparison value. 31 25 6.0 – Estimated standard score for the sample mean = ---------- = ----- = 10 0.6 Now we’ve got to figure out what to call this standard score. We can’t call it a value for Z because the number we’ve just calculated isn’t necessarily the real thing. It’s only an
But how did you get the standard error of the mean? You took the standard deviation of the population and divided it by the square root of the sample size. σ = Can you do that here? What problem do you run into? Well, to calculate the standard error of the mean you have to take the standard deviation of the population and divide it by the square root of N. But we don’t have σ. We don’t have the standard deviation of the population. If we don’t have that we can’t calculate σM, the standard error of the mean. If you don’t have σM you can’t calculate Z! If you can’t calculate Z, you can’t do a Z-test. Bummer. So what do you do! Clearly, we can’t do a Z-test. But that doesn’t mean we just have to give up. After all, we don’t have the standard deviation of the population, but we do have the next best thing. We’ve got an estimate of the standard deviation of the population. We’ve got the standard deviation of the sample. If we take the standard deviation of the sample and divide it by the square root of the sample size, we won’t get σM but we’ll have an estimate of σM. The symbol for an estimate of the standard error of the mean is S. S = Using the data provided above we get… S = = = = .6 Okay, so now we’ve got an estimate of how far off, on average, sample means are going to be off by when they’re trying to estimate that comparison value of 25. Now we can take our one difference from the comparison value, 31 – 25 = 6, and divide it by the average difference of sample means from this comparison value, 0.6. This will give us an estimate of the number of standard deviations that our sample mean above the comparison value. 31 – 25 6.0 Estimated standard score for the sample mean = ---------- = ----- = 10 0.6 Now we’ve got to figure out what to call this standard score. We can’t call it a value for Z because the number we’ve just calculated isn’t necessarily the real thing. It’s only an
One-sample%20t-test.docx