## 7.9 **Optional**: CI for mean differences (paired data)

*(Answers are available in Sect. A.7)*

Wave power has been considered as a source of energy since 1890, but the engineering necessary to successfully and practically harness this energy is complex.

To understand one method of harnessing this energy, one study (Hand et al. 1996) examined the bending stress (in Newton--metres) in part of a device used to generate electricity from wave power.

Two different mooring types were compared (Table 7.2) in 18 different sea states.

Method 1 | Method 2 | Differences |
---|---|---|

2.23 | 1.82 | 0.41 |

2.55 | 2.42 | 0.13 |

7.99 | 8.26 | -0.27 |

4.09 | 3.46 | 0.63 |

9.62 | 9.77 | -0.15 |

1.59 | 1.4 | 0.19 |

8.98 | 8.88 | 0.1 |

0.82 | 0.87 | -0.05 |

10.83 | 11.2 | -0.37 |

1.54 | 1.33 | 0.21 |

10.75 | 10.32 | 0.43 |

5.79 | 5.87 | -0.08 |

5.91 | 6.44 | -0.53 |

5.79 | 5.87 | -0.08 |

5.5 | 5.3 | |

9.96 | 9.82 | |

1.92 | 1.69 | |

7.38 | 7.41 |

- Explain
*why*these data should be analysed as mean differences. - Compute the sample differences (most have been done for you).
- Using the statistics mode on your calculator, compute the sample mean and the sample standard deviation of these differences.
- Compute the standard error of the mean difference. What does this value mean?
- Compute an approximate 95% confidence interval for the population mean difference in two methods.
- What conditions must be met for this CI to be statistically valid?
- Is it reasonable to assume the CI is statistically valid? Draw a stem-and-leaf plot to check.
- Do you think the mooring types are really different? Explain.

### References

Hand DJ, Daly F, Lunn AD, McConway KY, Ostrowski E. A handbook of small data sets. London: Chapman; Hall; 1996.