- The $t$ procedures assume that our data come from an SRS and will give trustworthy conclusions only if this condition is met.
- If your sample size is less than $15,$ the $t$ procedures yield trustworthy conclusions only if you can reasonably assume that your data comes from a normal distribution, that is, if the distribution appears to be symmetric with one peak and no outliers. If your data are obviously skewed or if there are any outliers, it is not advisable to use the $t$ procedures. Non-parametric or Bootstrap methods may be more advisable: try the a non-parametric confidence interval for estimating a population median or the One-Sample Bootstrap Confidence Interval Calculator for either a population mean or median.
- If your sample size is $15$ or larger, the $t$ procedures can be trusted if there are no outliers and the distribution is not obviously skewed.
- If your sample size is $40$ or larger, you may use $t$ procedures even if your distribution appears to be skewed.
| Data | |
| Sample data goes here (enter numbers in columns): | |
| Sample Mean: | $\bar{x}=$ |
| Sample Standard Deviation: | $s=$ |
| Sample Size: | $n=$ |
| Confidence Level: | |
| Use Summary Statistics: |
| Sample Size: | $n=$ |
| Degrees of Freedom: | $df=n-1=$ |
| Square Root of Sample Size: | $\sqrt{n}=$ |
| Mean: | $\overline{x}=$ |
| Sample Standard Deviation: | $s=$ |
| Critical $t$ Value: | $t^{*}=$ |
| Confidence Interval: |