Question

You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. dd denotes the mean of the difference between pre-test and post-test scores.

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:

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

49.3 | 31.9 |

47.1 | 27.5 |

42.6 | 40.9 |

42.2 | 43.4 |

41.5 | 39.1 |

41.8 | 52.5 |

33.5 | 17 |

42.9 | 40.1 |

33.5 | 31.6 |

39.8 | 57.2 |

47.1 | 45.7 |

46.5 | 50.9 |

51.7 | 52.4 |

58 | 61.3 |

47.5 | 54.9 |

- Make sure to choose the appropriate column for Sample 1 and 2 so that you are estimating the improved post-test score: μ2−μ1μ2-μ1

- What is the test statistic for this sample?

test statistic = Round to 3 decimal places. - What is the p-value for this sample? Round to 4 decimal
places.

p-value = - The p-value is...
- less than (or equal to) αα
- greater than αα

- This test statistic leads to a decision to...
- reject the null
- accept the null
- fail to reject the null

- As such, the final conclusion is that...
- There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.
- There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.
- The sample data support the claim that the mean difference of post-test from pre-test is less than 0.
- There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.

Answer #1

Observation Table:

post-test |
pre-test |
d=pre- post | |

49.3 | 31.9 | -17.4 | |

47.1 | 27.5 | -19.6 | |

42.6 | 40.9 | -1.7 | |

42.2 | 43.4 | 1.2 | |

41.5 | 39.1 | -2.4 | |

41.8 | 52.5 | 10.7 | |

33.5 | 17 | -16.5 | |

42.9 | 40.1 | -2.8 | |

33.5 | 31.6 | -1.9 | |

39.8 | 57.2 | 17.4 | |

47.1 | 45.7 | -1.4 | |

46.5 | 50.9 | 4.4 | |

51.7 | 52.4 | 0.7 | |

58 | 61.3 | 3.3 | |

47.5 | 54.9 | 7.4 | |

Mean (d)= | AVERAGE(C2:C16) | -1.24 | |

Sd (d)= | STDEV(C2:C16) | 10.2203 | |

P-value | TDIST(0.47,14,1) | 0.3228 |

Test statistic,

Degrees of freedom = n - 1 = 15 - 1 = 14

P-value = 0.3228

The p-value is greater than α.

This test statistic leads to a decision to fail to reject the null hypothesis.

The final conclusion is that, There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001. 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
pre-test and post-test samples for n=50n=50 subjects. The average
difference (post - pre) is ¯d=−6.7d¯=-6.7 with a standard deviation
of...

You wish to test the following claim (HaHa) at a significance
level of α=0.001α=0.001. For the context of this problem, the first
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you subtract.
Ho:μd=0Ho:μd=0
Ha:μd>0Ha:μd>0
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level of α=0.001α=0.001. 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
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distributed, but you do not know the standard deviation. You obtain
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level of α=0.01α=0.01. 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
pre-test and post-test samples for n=50n=50 subjects. The average
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deviation of the...

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level of α=0.02α=0.02. 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
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level of α=0.005α=0.005. For the context of this problem,
μd=PostTest−PreTestμd=PostTest-PreTest one data set represents a
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represents the pre and post test scores for an individual.
Ho:μd=0Ho:μd=0
Ha:μd≠0Ha:μd≠0
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distributed, but you do not know the standard deviation. You obtain
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pre-test
post-test
63.4
104.2
65.8
90...

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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
the following sample of data:
pre-test
post-test
33.5
58.5
36.4
10.8
47.5
16.5
54.4
21.8
51.7
55.5
38.9
71.5
39.1
31.1
40.9...

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level of α=0.05α=0.05. For the context of this problem,
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post-test. (Each row represents the pre and post test scores for an
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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 (Ha) at a significance
level of α=0.001. d denotes the mean of
the difference between pre-test and post-test scores.
Ho:μd=0
Ha:μd>0
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distributed, but you do not know the standard deviation. You obtain
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differences of sd=12.9 .
a.) The test statistic's value is
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level of α=0.01α=0.01. 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
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