Question

The paper "Lessons from Pacemaker Implantations" gave the results of a study that followed 89 heart patients who had received electronic pacemakers. The time (in months) to the first electrical malfunction of the pacemaker was summarized in the table below.

20 | 14 | 8 | 25 | 22 | 26 | 29 | 8 | 17 | 28 | 22 | 25 |

6 | 22 | 15 | 20 | 17 | 8 | 20 | 22 | 15 | 24 | 14 | 13 |

11 | 6 | 30 | 22 | 27 | 14 | 24 | 7 | 15 | 6 | 14 | 27 |

15 | 29 | 25 | 18 | 17 | 7 | 19 | 24 | 9 | 13 | 27 | 20 |

8 | 18 | 28 | 17 | 16 | 26 | 22 | 19 | 6 | 7 | 9 | 22 |

17 | 27 | 29 | 26 | 4 | 28 | 3 | 12 | 16 | 9 | 32 | 29 |

32 | 24 | 26 | 20 | 20 | 18 | 13 | 13 | 15 | 23 | 35 | 35 |

12 | 35 | 28 | 22 |
33 |

(a) Fill in the following table. (Round your answer to four decimal places if needed.)

Classes |
Frequency |
Relative Frequency |
Cumulative Relative Frequency |

0 - <6 | |||

6 - <12 | |||

12 - <18 | |||

18 - <24 | |||

24 - <30 | |||

30 - <36 |

(b) Use the cumulative relative frequencies to give approximate
answers to the following questions. (Round your answer to four
decimal places if needed.)

i. What proportion of those who participated in the study had
pacemakers that did not malfunction within the first year?

*p* =

ii. If the pacemaker must be replaced as soon as the first
electrical malfunction occurs, approximately what proportion
required replacement between 1 and 2 years after
implantation?

*p* =

(c) Construct a cumulative relative frequency plot. Prepare an
Excel document. The file should be named with a .xls
extension.

Use it to answer the following questions. (Round your answers to
the nearest whole number if needed.)

i. What is the approximate time at which about 50% of the
pacemakers had failed?

*t* = months

ii. What is the approximate time at which only about 10% of the
pacemakers initially implanted were still functioning?

*t* = months

Answer #1

(a)

Class interval | Frequency | Relative frequency | Cumulative Relative Frequency |

0 - <6 | 2 | 2 / 89 = 0.0225 | 0.0225 |

6 - <12 | 15 | 15 / 89 = 0.1685 | 0.1910 |

12 - <18 | 22 | 22 / 89 = 0.2472 | 0.4382 |

18 - <24 | 20 | 20 / 89 = 0.2247 | 0.6629 |

24 - <30 | 23 | 23 / 89 = 0.2584 | 0.9213 |

30 - <36 | 7 | 7 / 89 = 0.0787 | 1.0000 |

(b) i.
proportion of pacemakers that did not malfunction within the first
year = 1 - 0.1910 = **0.8090**

ii. proportion required replacement between 1 and 2 years after implantation = 0.6629 - 0.1910

=
**0.4719**

--

(c) I. approximate time at which about 50% of the pacemakers had failed.

*t* = **20** months

ii. approximate time at which only about 10% of the pacemakers
initially implanted were still functioning?

*t* = **28** months

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Number of Days (frequency)
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9
0.25 to <0.35
19
0.35 to <0.45
28
0.45 to <0.50
24
0.50 to <0.55
39
0.55 to <0.60
52
0.60 to <0.65
96
0.65 to <0.70
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0.70 to <0.75
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X
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Y
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X
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30
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39
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30
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24
26
24
22
25
5
22
24
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51
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