We utilize the t-distribution to create a more exact confidence interval.įurther, the confidence interval for the mean based on the t-distribution typically works well even when the population isn’t normally distributed, unless the population distribution is highly skewed and the sample size (n) is very small. However, with access to Minitab and incredible computing power, settling for an approximation is unnecessary. it is much easier to look up a z-multiplier than a t-multiplier when using tables.
CALCULALTING CONFIDENCE AND PREDICTION INTERVALS MINITAB 18 MANUAL
That approximation is helpful in academic settings that require manual calculations, e.g. In those cases, even when the sample size is “large” (n > 30-40 in most introductory statistics books), the sample mean is approximately normally distributed.
In the vast majority of cases, we have to estimate the standard deviation from the sample data, just as we do the mean. That’s a helpful academic consideration when learning about confidence intervals, but, in practice, we almost never know the true standard deviation. The sample mean has an exact standard normal (Z) distribution when the population from which the sample is selected is normally distributed with known standard deviation. Can anyone explain why, though? I’m just curious, that’s all. Now that I know this, I’ll be aware of it. Weird, right? So, I recalculated the CI again, by hand (remember, glutton for punishment), but this time I used the Student t-distribution and realized that, even though the sample is greater than 30, Minitab used the Student t-distribution to calculate the CI. However, when I plugged this same data into Minitab and ran a Graphical Summary (Stat > Basic Statistics > Graphical Summary), it gave me the following: UL=$101.06 and LL=$67.87. I got an Upper Limit of $99.94 and a Lower Limit of $69.00. Therefore, I can use z-distribution table. Rationale: Dataset sample is large (n>=30) and data is normal (Minitab normality test rejected the null hypothesis). Glutton for punishment, I guess.) In any case, my dataset has over 30 records, therefore, I was using the z-table to calculate the CI. (Please don’t ask why I’m hand calculating this stuff. As I was playing around in Minitab 17 today, I noticed that my hand-calculated confidence interval (CI) for a dataset did not match the CI that Minitab calculated for the same dataset.
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