To see if a new training program is effective, you have employees take a pre-test before training and a post-test after training. If the post-test scores are significantly improved, you can conclude the training program is effective.

Conduct a hypothesis test for the null hypothesis that there is no significant improvement using the paired t-test with alpha = 0.05.

Use the data in this table:

Pre-test Score | Post-test Score | Improvement |

51 | 59 | 8 |

58 | 83 | 25 |

66 | 51 | -15 |

40 | 51 | 11 |

47 | 66 | 19 |

74 | 96 | 22 |

38 | 85 | 47 |

What is the value of the test statistic, ?

What is the value associated with the critical region, ?

If you would reject the null hypothesis, enter 1;

If you would fail to reject the null hypothesis, enter 2.

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