Question

For the data in the table below, assume a uniform distribution. Estimate the parameters for this distribution, and perform a Chi Squared goodness of fit test on what is assumed to be a uniform distribution.

6.40 |
4.39 |
6.86 |
5.24 |
4.01 |

5.54 |
4.50 |
5.69 |
5.85 |
5.42 |

5.94 |
6.78 |
6.52 |
5.82 |
6.46 |

4.65 |
4.20 |
5.25 |
6.58 |
4.73 |

6.53 |
4.99 |
5.90 |
5.51 |
6.50 |

Answer #1

The null hypothesis

H0: the data follow uniform distribution

Test statistic

where

Oi : observed frequency

Ei : expected frequency

First we find sample mean = (6.40+.....+6.50)/25 = 5.61

For Uniform distribution ,each observation has a equal probability and therefore equal expected frequency

Calculation

Oi | Ei | (Oi-Ei)^2/Ei | |

4.01 | 5.6104 | 0.45652363 | |

4.2 | 5.6104 | 0.35456084 | |

4.39 | 5.6104 | 0.26546702 | |

4.5 | 5.6104 | 0.21976832 | |

4.65 | 5.6104 | 0.16440328 | |

4.73 | 5.6104 | 0.13815488 | |

4.99 | 5.6104 | 0.06860405 | |

5.24 | 5.6104 | 0.0244539 | |

5.25 | 5.6104 | 0.02315132 | |

5.42 | 5.6104 | 0.0064616 | |

5.51 | 5.6104 | 0.00179669 | |

5.54 | 5.6104 | 0.00088339 | |

5.69 | 5.6104 | 0.00112936 | |

5.82 | 5.6104 | 0.00783049 | |

5.85 | 5.6104 | 0.01023245 | |

5.9 | 5.6104 | 0.0149487 | |

5.94 | 5.6104 | 0.01936335 | |

6.4 | 5.6104 | 0.11112722 | |

6.46 | 5.6104 | 0.12865752 | |

6.5 | 5.6104 | 0.14105735 | |

6.52 | 5.6104 | 0.14747115 | |

6.53 | 5.6104 | 0.15073153 | |

6.58 | 5.6104 | 0.16756812 | |

6.78 | 5.6104 | 0.24382649 | |

6.86 | 5.6104 | 0.27832243 | |

total | 3.14649508 |

Therefore ,

degrees of freedom = 25-1=24

P value = 1.000

Since P value > 0.05

The result is not significant

We fail to reject H0

There is not sufficient evidence to conclude that the sample data do not follow uniform distribution .

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