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The one sample test of means compares an unknown mean, \(\mu\), to a fixed value, \(\mu_0\).

The statistical test used for this set of hypotheses can be a \(t\)-test or a \(z\)-test, depending on if the standard deviation is a known value or estimated from the sample.

To input multiple values, seperate them by a comma.

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- Solve For
- The unknown you are interested in solving for.
- N
- The sample size used to test the hypothesis.
- Alpha
- The \(\alpha\) (Type I error rate) level of the hypothesis test.
- Power
- The power (1 - Type II error rate) of the hypothesis test.
- Unknown Mean \(\mu\)
- The mean of the sample. If you are comparing a difference in means to zero, set this value to the difference.
- Null Mean \(\mu_0\)
- The mean against which the unknown mean is compared to. If you are comparing a difference in means to zero, set this value to zero.
- Standard Deviation
- The standard deviation of the sample.
- Known Standard Deviation
- If the standard deviation is known or estimated (usually it is estimated).
- Margin
- The margin is a value the effect size needs to exceed to be meaningful. For hypotheses of equivalence, the margin must be greater than 0, or the calculation will not be solvable. For one sided tests, a margin is less than 0 implies a non-inferiority hypothesis. Otherwise, a superiority hypothesis is implied. Read More
- Hypothesis
- There are three types of hypotheses that can be tested:
*two-sided*,*one-sided*and*equivalence*. Tests of equivalence must include a margin if the unknown and null means are equal. Read More

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Hypothesis: {{ hypothesis }}

Known Standard Deviation

Unknown Standard Deviation

N | Alpha | Power | Alt. Mean \(\mu\) | Null Mean \(\mu_0\) | Standard Deviation | Margin |
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- Chow, S., Shao, J., & Wang, H. (2003),
*Sample size calculations in clinical research,*New York: Marcel Dekker.