Question

A drug company is developing a product which is intended to shorten the duration of colds. To determine if the product is effective, a study is done with two groups of physiologically similar people. The placebo group is given a sugar pill, the treatment group is given the cold remedy, and the results are given below.

Cold duration (days) | Placebo group (relative frequency) | Treatment group (frequency) |

0-5 days | 40% | 102 |

6-9 days | 35% | 70 |

10-12 days | 15% | 14 |

13+ days | 10% | 14 |

We want to determine whether or not there is a significant difference in the distribution of the cold durations between the placebo group and the treatment group. Use α = .01 to make your conclusion.

The value of the chi-square statistic is:

The p-value of the test is:

Answer #1

applying chi square test:

relative | observed | Expected | residual | Chi square | |

category | frequency |
O_{i} |
E_{i}=total*p |
R^{2}_{i}=(O_{i}-E_{i})/√E_{i} |
R^{2}_{i}=(O_{i}-E_{i})^{2}/E_{i} |

1 | 0.400 | 102 | 80.00 | 2.46 | 6.050 |

2 | 0.350 | 70 | 70.00 | 0.00 | 0.000 |

3 | 0.150 | 14 | 30.00 | -2.92 | 8.533 |

4 | 0.100 | 14 | 20.00 | -1.34 | 1.800 |

total | 1.000 | 200 | 200 | 16.383 |

value of the chi-square statistic =16.3833

p-value of the test is =0.0009

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