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Confidence interval (CI)
Formula
Notation
| Term | Description |
|---|---|
| sd |  |
 | Σd / n |
| d | x1 - x2 and x1 and x2 are paired observations from populations 1 and 2, respectively |
| tα/2 | the inverse cumulative probability of a t distribution with n-1 degrees of freedom at 1-α/2 |
| α | 1 - confidence level/100 |
| n | Sample size of the pairs of observations |
T-value
Formula
Notation
| Term | Description |
|---|---|
| μ0 | hypothesized population mean of the differences |
 | mean of the paired sample differences |
| sd | sample standard deviation of the paired sample differences |
| n | Sample size of the pairs of observations |
Degrees of freedom (DF)
Applies to: Minitab web app
Formula
Notation
| Term | Description |
|---|---|
| v | Degrees of freedom |
| n | Sample size of the pairs of observations |
P-value
The calculation for the p-value depends on the alternative hypothesis.
| Alternative Hypothesis | P-value |
|---|---|
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Notation
| Term | Description |
|---|---|
| μd | population mean for the sample of differences |
| μ0 | hypothesized population mean for the sample of differences |
| t | t-statistic of the sample data |
| tn-1 | a random variable from the t-distribution with n-1 degrees of freedom |
| n | Sample size of the pairs of observations |
