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A metallurgical engineer wants to determine whether the median chromium content in a set of stainless steel samples is equal to 18%. The engineer randomly selects 12 samples and measures the chromium content.
The engineer performs a 1-sample sign test to determine whether the median chromium content differs from 18%.
The null hypothesis states that the median chromium content equals 18%. Because the p-value is 0.388, which is greater than the significance level of 0.05, the engineer cannot reject the null hypothesis. The engineer does not have enough evidence to conclude that the median chromium content differs from 18%.
| Sample | N | Median |
|---|---|---|
| %Chromium | 12 | 17.7 |
| Null hypothesis | H₀: η = 18 |
|---|---|
| Alternative hypothesis | H₁: η ≠ 18 |
| Sample | Number < 18 | Number = 18 | Number > 18 | P-Value |
|---|---|---|---|---|
| %Chromium | 8 | 0 | 4 | 0.388 |
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