Question

Students in a semester-long health-fitness program have their
percentage of body fat measured at the beginning of the semester
and at the end of the semester. Assume that the percentages of body
fat follow normal distributions. Find a 95% confidence interval
for, μ Pre-program % 11 12 19 12 15 14 11 13 14 Post-program % 9 10 16 9 15 12 10 11 11 |

Answer #1

Pre | Post | Post - Pre |

11 | 9 | -2 |

12 | 10 | -2 |

19 | 16 | -3 |

12 | 9 | -3 |

15 | 15 | 0 |

14 | 12 | -2 |

11 | 10 | -1 |

13 | 11 | -2 |

14 | 11 | -3 |

sample mean, xbar = -2

sample standard deviation, s = 1

sample size, n = 9

degrees of freedom, df = n - 1 = 8

Given CI level is 95%, hence α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.306

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))

CI = (-2 - 2.306 * 1/sqrt(9) , -2 + 2.306 * 1/sqrt(9))

CI = (-2.77 , -1.23)

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