Question

*Metal Tags on Penguins*

A test is performed for the difference in the proportion of
penguins who survive over a 10-year period, between penguins tagged
with metal tags and those tagged with electronic tags. We are
interested in testing whether the type of tag has an effect on
penguin survival rate, this time using a chi-square test. In the
study, 34 of the 154 metal-tagged penguins survived while 61 of the
177 electronic-tagged penguins survived.

(a) Create a two-way table from the information given.

Metal | Electronic | Total | |
---|---|---|---|

Survived | Enter your answer in accordance to item (a) of the question statement | Enter your answer in accordance to item (a) of the question statement | Enter your answer in accordance to item (a) of the question statement |

Died | Enter your answer in accordance to item (a) of the question statement | Enter your answer in accordance to item (a) of the question statement | Enter your answer in accordance to item (a) of the question statement |

Total | Enter your answer in accordance to item (a) of the question statement | Enter your answer in accordance to item (a) of the question statement | Enter your answer in accordance to item (a) of the question statement |

(b) Give a table with the expected counts for each of the four
categories.

Round your answers to two decimal places.

Metal | Electronic | |

Survived | Enter your answer in accordance to item (b) of the question statement | Enter your answer in accordance to item (b) of the question statement |

Died | Enter your answer in accordance to item (b) of the question statement | Enter your answer in accordance to item (b) of the question statement |

(c) Calculate the chi-square test statistic.

Round your answer to one decimal place.

chi-square statistic = Enter your answer in accordance to item
(c) of the question statement

(d) Determine the *p*-value and state the conclusion.

Round your answer to three decimal places.

*p*-value = Enter your answer in accordance to item (d) of
the question statement

Conclusion: Choose the answer from the menu in accordance to item
(d) of the question statement
RejectDo not reject H0.

Is survival rate related to the type of tag?

Choose the answer from the menu in accordance to item (d) of the
question statement
YesNo

Answer #1

a)

Oi |
Metal | Electronic | Total |

survived | 34 | 61 | 95 |

Died | 120 | 116 | 236 |

total | 154 | 177 | 331 |

b)

E_{i}=row total*column
total/grand total |
Metal | Electronic |

survived | 44.20 | 50.80 |

Died | 109.80 | 126.20 |

c)

applying chi square test:

chi square χ^{2} |
=(O_{i}-E_{i})^{2}/E_{i} |
Metal | Electronic | Total |

survived | 2.3536 | 2.0478 | 4.401 | |

Died | 0.9474 | 0.8243 | 1.772 | |

total | 3.301 | 2.872 | 6.173 |

chi-square test statistic =6.2

d)

p value =0.013

reject Ho , if level of significance is greater than 0.013

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We are interested in testing whether the type of tag has an
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In the study, 33 of the 167 metal-tagged penguins survived while 68
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