Question

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day ("Activities of dolphin," 2013). The numbers in table #11.1.6 represent the number of groups of dolphins that were partaking in an activity at certain times of days. Is there enough evidence to show that the activity and the time period are independent for dolphins? Test at the 1% level.

**Table #11.1.6: Dolphin Activity**

Activity |
Period |
Row Total |
|||

Morning |
Noon |
Afternoon |
Evening |
||

Travel |
6 |
6 |
14 |
13 |
39 |

Feed |
28 |
4 |
0 |
56 |
88 |

Social |
38 |
5 |
9 |
10 |
62 |

Colunm Total |
72 |
15 |
23 |
79 |
189 |

Answer #1

The hypothesis being tested is:

H_{0}: Activity and the time period are independent

H_{a}: Activity and the time period are not
independent

Morning | Noon | Afternoon | Evening | Total | ||

Travel | Observed |
6 |
6 |
14 |
13 |
39 |

Expected | 14.86 | 3.10 | 4.75 | 16.30 | 39.00 | |

O - E | -8.86 | 2.90 | 9.25 | -3.30 | 0.00 | |

(O - E)² / E | 5.28 | 2.73 | 18.04 | 0.67 | 26.72 | |

Feed | Observed |
28 |
4 |
0 |
56 |
88 |

Expected | 33.52 | 6.98 | 10.71 | 36.78 | 88.00 | |

O - E | -5.52 | -2.98 | -10.71 | 19.22 | 0.00 | |

(O - E)² / E | 0.91 | 1.28 | 10.71 | 10.04 | 22.93 | |

Social | Observed |
38 |
5 |
9 |
10 |
62 |

Expected | 23.62 | 4.92 | 7.54 | 25.92 | 62.00 | |

O - E | 14.38 | 0.08 | 1.46 | -15.92 | 0.00 | |

(O - E)² / E | 8.76 | 0.00 | 0.28 | 9.77 | 18.81 | |

Total | Observed | 72 | 15 | 23 | 79 | 189 |

Expected | 72.00 | 15.00 | 23.00 | 79.00 | 189.00 | |

O - E | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |

(O - E)² / E | 14.95 | 4.00 | 29.03 | 20.48 | 68.46 | |

68.46 | chi-square | |||||

6 | df | |||||

8.44E-13 | p-value |

Since the p-value (0.0000) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we cannot conclude that the activity and the time period are independent for dolphins.

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