Example of 1-Sample Sign

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%.

  1. Open the sample data, StainlessSteelComposition.MTW.
  2. Choose Stat > Nonparametrics > 1-Sample Sign.
  3. In Variables, enter %Chromium.
  4. Select Test median and enter 18.
  5. Click OK.

Interpret the results

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%.

Sign Test for Median: %Chromium

Method η: median of %Chromium
Descriptive Statistics Sample N Median %Chromium 12 17.7
Test 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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