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# Elem Stats ch 9

### A Brief Version: Elementary Statistics Ch 9

Question | Answer |
---|---|

What are the assumptions for the test to determine the Difference Between Two Means? | The samples must be independent of each other. The standard deviation of both populations must be known, and if the sample sizes are less than 30, the populations must be normally or approximately normally distributed. |

Independent Samples | There is no relationship between the subjects in each sample. |

Pooled Estimate of the Variance | A weighted average of the variance using the two sample variances and the degrees of freedom of each variance as the weights. |

Dependent Samples | When subjects or samples are paired or matched in some way. |

D bar | The mean of the differences. |

s sub d | The standard deviation of the differences. |

D = | The differences of the values of the pairs of data. |

What are the characteristics of the F distribution? | The vales of F cannot be negative. The distribution is positively skewed. The mean value of F is approximately equal to 1. It is a family of curves based on the degrees of freedom of the variance of the numerator and the denominator. |

F Test | Comparison of two variances or standard deviations. |

What are the notes for the use of the F test? | The largest variance should always be placed in the numerator of the formula regardless of the subscripts. For a two-tailed test the alpha value must be divided by 2 and the critical value placed on the right side of the curve. |

What are the assumptions for testing the Differences Between Two Variances? | The populations from which the samples were obtained must be normally distributed. The samples must be independent of each other. |

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dengler