In the summer of 2007 a pretest in mathematics was given to prejuniors in a UB program. At the end of the summer term a posttest was given. The results are seen in the table.

Pretest | Posttest |
---|---|

10 | 16 |

5 | 13 |

5 | 5 |

9 | 19 |

10 | 15 |

6 | 19 |

3 | 10 |

8 | 13 |

9 | 11 |

8 | 15 |

5 | 10 |

4 | 12 |

7 | 16 |

6 | 17 |

9 | 18 |

6 | 13 |

8 | 18 |

7 | 8 |

8 | 19 |

11 | 11 |

12 | 12 |

6 | 11 |

7 | 11 |

9 | 17 |

7 | 10 |

11 | 14 |

16 | 18 |

10 | 15 |

6 | 18 |

- _________ Calculate the sample mean x for the pretest.
- _________ Calculate the sample mean x for the posttest.
- _________ Are the sample means for the two samples mathematically different?
- __________________ What is the p-value? Use the difference of means for paired data TTEST function =TTEST(data_range_x;data_range_y;2;1)to determine the p-value for this paired two sample data.
- __________________ Is the difference in the means statistically significant at a risk of a type I error alpha α = 0.05?
- __________________ Would we "fail to reject" or "reject" a null hypothesis of no difference in the mean between the pretest and posttest?
- __________________ What is the maximum level of confidence we can have that the difference is statistically significant?

Hypothesis Testing | |||
---|---|---|---|

Statistic or Parameter | Symbol | Equations | OpenOffice |

Relationship between confidence level c and alpha α for two-tailed tests | 1 − c = α | ||

Calculate t-critical for a two-tailed test | t_{c} | =TINV(α;df) | |

Calculate a t-statistic t | t | =(x - μ)/(sx/SQRT(n)) | |

Calculate a two-tailed p-value from a t-statistic | p-value | = TDIST(ABS(t);df;2) | |

Calculate a p-value for the difference of the means from two samples of paired samples | =TTEST(data_range_x;data_range_y;2;1) | ||

Calculate a p-value for the difference of the means from two independent samples, no presumption that σ_{x} = σ_{y} |
=TTEST(data_range_x;data_range_y;2;3) |