In: Statistics and Probability

Researchers at a cardiovascular institute are concerned about the association between exercise and hypertension among their patient population. Suppose in order to assess this relationship, the researchers conducted a study where a population of 35-55 year old participants were enrolled and followed for a period of 10 years, and required to submit weekly diary submissions about their exercise routines. The researchers then conducted clinic visits where blood pressure was measured and hypertensive status was confirmed. Suppose the following table illustrates the relationship when exercise habits are categorized into the following groups. Hypertension No Hypertension Total No Exercise 105 115 220 Exercise 1-2 x Week 101 305 406 Exercise more than 2 x per Week 13 143 156 Total 219 563 782 a) Carry out a formal test to determine if there is a difference in the outcome between the various exercise categories. Write out your null and alternative hypotheses and interpret your results with 95% confidence.

The hypothesis being tested is:

H0: There is no difference in the outcome between the various exercise categories

Ha: There is a difference in the outcome between the various exercise categories

Col 1 | Col 2 | Total | ||

Row 1 | Observed |
105 |
115 |
220 |

Expected | 61.61 | 158.39 | 220.00 | |

O - E | 43.39 | -43.39 | 0.00 | |

(O - E)² / E | 30.56 | 11.89 | 42.44 | |

Row 2 | Observed |
101 |
305 |
406 |

Expected | 113.70 | 292.30 | 406.00 | |

O - E | -12.70 | 12.70 | 0.00 | |

(O - E)² / E | 1.42 | 0.55 | 1.97 | |

Row 3 | Observed |
13 |
143 |
156 |

Expected | 43.69 | 112.31 | 156.00 | |

O - E | -30.69 | 30.69 | 0.00 | |

(O - E)² / E | 21.56 | 8.39 | 29.94 | |

Total | Observed | 219 | 563 | 782 |

Expected | 219.00 | 563.00 | 782.00 | |

O - E | 0.00 | 0.00 | 0.00 | |

(O - E)² / E | 53.53 | 20.82 | 74.35 | |

74.35 | chi-square | |||

2 | df | |||

7.15E-17 | p-value |

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference in the outcome between the various exercise categories.

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