Complete the following steps to interpret a 1-sample sign test. Key output includes the estimate of the median, the confidence interval, and the p-value.

First, consider the sample median, and then examine the confidence interval.

The median of the sample data is an estimate of the population median. Because the median is based on sample data and not on the entire population, it is unlikely that the sample median equals the population median. To better estimate the population median, use the confidence interval.

The confidence interval provides a range of likely values for the population median. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population median. The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size.

The 1-sample sign test does not always achieve the confidence level that you specify because the sign test statistic is discrete. Because of this, Minitab calculates 3 confidence intervals with varying levels of precision. You should use the shortest interval for which the achieved confidence level is closest to the target confidence level.

To get both the confidence interval and the test results you must perform the analysis twice because Minitab only calculates one item at a time.

Sample | N | Median |
---|---|---|

%Chromium | 12 | 17.7 |

Sample | CI for η | Achieved Confidence | Position |
---|---|---|---|

%Chromium | (17.5, 18.1) | 85.40% | (4, 9) |

(17.4263, 18.7632) | 95.00% | Interpolation | |

(17.4, 19) | 96.14% | (3, 10) |

In these results, the estimate of the population median for the percentage of chromium is 17.7. You can use the second interval because it is the shortest interval that has a confidence interval closest to the target of 95%. You can be 95% confident that the population median is between 17.43 and 18.76.

To determine whether the difference between the population median and the hypothesized median is statistically significant, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.

- P-value ≤ α: The difference between the medians is significantly different (Reject H
_{0}) - If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis. You can conclude that the difference between the population median and the hypothesized median is statistically significant. Use your specialized knowledge to determine whether the difference is practically significant. For more information, go to Statistical and practical significance.
- P-value > α: The difference between the medians is not significantly different (Fail to reject H
_{0}) - If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the population median is significantly different from the hypothesized median. You should make sure that your test has enough power to detect a difference that is practically significant.

To get both the confidence interval and the test results you must perform the analysis twice because Minitab only calculates one item at a time.

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 |

In these 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, you fail to reject the null hypothesis. You cannot conclude that the population median chromium content differs from 18%.