Question

Many statistical procedures require that we draw a sample from a population whose distribution is approximately normal. Often we don’t know whether the population is approximately normal when we draw the sample. So the only way we assess whether the population is approximately normal is to examine its sample. Assessing normality is more important for small samples. Below, you’ll see some small samples and you’ll be asked to assess whether the populations they are drawn from can be treated as approximately normal.

- The following data set is given. Determine whether it is reasonable to treat the following sample as though it comes from an approximately normal population. Include any charts or graphs you make in Excel here and justify your answer.

2.6 |
4.2 |
1.5 |
2.0 |
0.6 |
0.7 |
6.6 |

2.2 |
9.7 |
1.8 |
4.2 |
4.4 |
0.6 |
0.2 |

Answer #1

Theoritical Quantile | Actual Quantile | ||

1 | 0.066667 | -1.501086 | 0.2 |

2 | 0.133333 | -1.110772 | 0.6 |

3 | 0.2 | -0.841621 | 0.6 |

4 | 0.266667 | -0.622926 | 0.7 |

5 | 0.333333 | -0.430727 | 1.5 |

6 | 0.4 | -0.253347 | 1.8 |

7 | 0.466667 | -0.083652 | 2 |

8 | 0.533333 | 0.0836517 | 2.2 |

9 | 0.6 | 0.2533471 | 2.6 |

10 | 0.666667 | 0.4307273 | 4.2 |

11 | 0.733333 | 0.6229257 | 4.2 |

12 | 0.8 | 0.8416212 | 4.4 |

13 | 0.866667 | 1.1107716 | 6.6 |

14 | 0.933333 | 1.5010859 | 9.7 |

From the QQ plot, we can conclude that the given sample does not follow the normal distribution. Because the points at the tails have deviated from the straight line.

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