Question

You wish to test the following claim (HaHa) at a significance
level of α=0.002α=0.002. For the context of this problem,
μd=PostTest−PreTestμd=PostTest-PreTest where the first data set
represents a pre-test and the second data set represents a
post-test. (Each row represents the pre and post test scores for an
individual. Be careful when you enter your data and specify what
your μ1μ1 and μ2μ2 are so that the differences are computed
correctly.)

Ho:μd=0Ho:μd=0

Ha:μd≠0Ha:μd≠0

You believe the population of difference scores is normally
distributed, but you do not know the standard deviation. You obtain
the following sample of data:

pre-test | post-test |
---|---|

38.5 | 44.5 |

34.8 | 42 |

39.9 | 6.6 |

51.5 | 38.9 |

30.5 | 29.2 |

47 | 121.8 |

34 | 20 |

40.1 | 79.7 |

45.4 | -9 |

38.5 | 70.9 |

35 | 23.7 |

32.6 | -27.8 |

44.3 | 150.3 |

38.2 | 66.6 |

44.1 | -19.7 |

48 | 126.2 |

What is the test statistic for this sample?

test statistic = (Report answer accurate to 4 decimal
places.)

What is the p-value for this sample?

p-value = (Report answer accurate to 4 decimal
places.)

Answer #1

H0:μd = 0

Ha:μd ≠ 0

Pre-test | Post-test | Difference (d) | (d-Mean)^2 |

38.5 | 44.5 | -6 | 2.54 |

34.8 | 42 | -7.2 | 0.16 |

39.9 | 6.6 | 33.3 | 1672.30 |

51.5 | 38.9 | 12.6 | 407.79 |

30.5 | 29.2 | 1.3 | 79.10 |

47 | 121.8 | -74.8 | 4516.68 |

34 | 20 | 14 | 466.29 |

40.1 | 79.7 | -39.6 | 1024.40 |

45.4 | -9 | 54.4 | 3843.23 |

38.5 | 70.9 | -32.4 | 615.35 |

35 | 23.7 | 11.3 | 356.97 |

32.6 | -27.8 | 60.4 | 4623.15 |

44.3 | 150.3 | -106 | 9683.79 |

38.2 | 66.6 | -28.4 | 432.90 |

44.1 | -19.7 | 63.8 | 5097.07 |

48 | 126.2 | -78.2 | 4985.24 |

Total | -121.5 | 37806.95 |

Σd = -121.5

n = 16

d̅ = Σd/n = -121.5/16=-7.59

sd = (Σ(d-d̅)2/(n-1))^0.5

= (37806.95/15)^0.5

= 50.2

Test statistic: t = (d̅-D)/(sd/n^0.5) = (-7.59-0)/(50.2/16^0.5) = -0.61

Critical value (Using Excel function T.INV.2T(probability,n-1)) = T.INV.2T(0.05,15) = 2.13

Since test statistic is less than critical value, we do not reject the null hypothesis and conclude that μd = 0.

You wish to test the following claim (HaHa) at a significance
level of α=0.002α=0.002. For the context of this problem,
μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and
the second data set represents a post-test.
Ho:μd=0Ho:μd=0
Ha:μd>0Ha:μd>0
You believe the population of difference scores is normally
distributed, but you do not know the standard deviation. You obtain
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You wish to test the following claim (HaHa) at a significance
level of α=0.005α=0.005. For the context of this problem,
μd=PostTest−PreTestμd=PostTest-PreTest one data set represents a
pre-test and the other data set represents a post-test. Each row
represents the pre and post test scores for an individual.
Ho:μd=0Ho:μd=0
Ha:μd≠0Ha:μd≠0
You believe the population of difference scores is normally
distributed, but you do not know the standard deviation. You obtain
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level of α=0.002α=0.002. For the context of this problem, μd =
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Ho:μd=0
Ha:μd<0
You believe the population of difference scores is normally
distributed, but you do not know the standard deviation. You obtain
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You wish to test the following claim (HaHa) at a significance
level of α=0.05α=0.05. For the context of this problem,
μd=PostTest−PreTestμd=PostTest-PreTest where the first data set
represents a pre-test and the second data set represents a
post-test. (Each row represents the pre and post test scores for an
individual. Be careful when you enter your data and specify what
your μ1μ1 and μ2μ2 are so that the differences are computed
correctly.)
Ho:μd=0Ho:μd=0
Ha:μd≠0Ha:μd≠0
You believe the population of difference scores...

You wish to test the following claim (HaHa) at a significance
level of α=0.005α=0.005. For the context of this problem,
μd=PostTest−PreTestμd=PostTest-PreTest one data set represents a
pre-test and the other data set represents a post-test. Each row
represents the pre and post test scores for an individual.
Ho:μd=0Ho:μd=0
Ha:μd≠0Ha:μd≠0
You believe the population of difference scores is normally
distributed, but you do not know the standard deviation. You obtain
the following sample of data:
pre-test
post-test
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You wish to test the following claim (HaHa) at a significance
level of α=0.005α=0.005. For the context of this problem,
μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and
the second data set represents a post-test.
Ho:μd=0Ho:μd=0
Ha:μd>0Ha:μd>0
You believe the population of difference scores is normally
distributed, but you do not know the standard deviation. You obtain
the following sample of data:
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