Question

Pilates is a popular set of exercises for the treatment of individuals with lower back pain. The method has six basic principles: centering, concentration, control, precision, flow, and breathing. An article reported on an experiment involving 88 subjects with nonspecific low back pain. The participants were randomly divided into two groups of equal size. The first group received just educational materials, whereas the second group participated in 6 weeks of Pilates exercises. The sample mean level of pain (on a scale from 0 to 10) for the control group at a 6-week follow-up was 5.1 and the sample mean for the treatment group was 3.2; both sample standard deviations were 2.3.

Calculate the test statistic and *P*-value. (Round your
test statistic to two decimal places and your *P*-value to
four decimal places.)

Does it appear that true average pain level for the control condition exceeds that for the treatment condition by more than 1 at a significance level of 0.01? Carry out a test of appropriate hypotheses.

Calculate the test statistic and *P*-value. (Round your
test statistic to two decimal places and your *P*-value to
four decimal places.)

Answer #1

Two-Sample T-Test and CI

Method

μ1: mean of Sample 1 |

µ2: mean of Sample 2 |

Difference: μ1 - µ2 |

Equal variances are assumed for this analysis.

Descriptive Statistics

Sample | N | Mean | StDev | SE Mean |

Sample 1 | 44 | 5.10 | 2.30 | 0.35 |

Sample 2 | 44 | 3.20 | 2.30 | 0.35 |

Estimation for Difference

Difference |
Pooled StDev |
95% Lower Bound for Difference |

1.900 | 2.300 | 1.085 |

Test

Null hypothesis | H0: μ1 - µ2 = 1 |

Alternative hypothesis | H1: μ1 - µ2 > 1 |

T-Value | DF | P-Value |

1.84 | 86 | 0.0350 |

Since p-value is more than level of significance 0.01 we fail to reject null hypothesis and there is no significance evidence to conclude that the true average pain level for the control condition exceeds that for the treatment condition by more than 1 at a significance level of 0.01.

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