Question

Find the 95% confidence interval for the difference between two means based on this information about two samples. Assume independent samples from normal populations. (Use conservative degrees of freedom.) (Give your answers correct to two decimal places.)

Sample | Number | Mean | Std. Dev. |

1 | 17 | 40 | 26 |

2 | 30 | 26 | 27 |

Lower Limit | |

Upper Limit |

You may need to use the appropriate table in Appendix B to answer
this question.

Answer #1

Formula for Confidence Interval for Difference in two Population means when population Standard deviation are not known (non pooled)

(Conservative)

n_{1} : Sample Size of Sample 1 |
17 |

n_{2} : Sample Size of Sample 2 |
30 |

: Sample Mean of Sample 1 | 40 |

: Sample Mean of Sample 2 | 26 |

s_{1} : Sample Standard Deviation of Sample 1 |
26 |

s_{2} : Sample Standard Deviation of Sample 2 |
27 |

Confidence Level | 95% |

\alpha (= 100-95/100=5/100 ) = 0.05 |
0.05 |

\alpha/2 (=0.05/2=0.025) |
0.025 |

Degrees of Freedom : =Min(17-1,30-1) | 16 |

2.1199 |

95% confidence interval for the difference between two means

Lower Limit - 2.97

Upper Limit 30.97

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