Question

Let µ1, µ2, and µ3 be the means of normal distributions with a common but unknown variance. We want to test H0 : µ1 = µ2 = µ3 against Ha : at least two µj are different, by taking random samples of size 4 from each distributions. Let PP x1· = 28, x2· = 46, x3· = 34, and x 2 ij = 1038.

(a) Construct an ANOVA table. (b) Carry out the 5% significance level test. (c) What is the HSD in this problem?

Answer #1

From the given data,

a)

X | n | n*(x - xgrand)² | |

Group1 | 28 | 4 | 256 |

Group 2 | 46 | 4 | 400 |

Group 3 | 34 | 4 | 16 |

xgrand | 36 | ||

sum=672 |

Source | SS | df | MS | F | P-Value |

Between | 672 | 2 | 336 | 8.262295 | 0.009179 |

Error | 366 | 9 | 40.66667 | ||

Total | 1038 | 11 |

b)

Hypothesis :

H_{0}: µ_{1} = µ_{2} = µ_{3}

H_{a}: Not all means are equal

The p-value is 0.009179.

Since the p-value (0.009179) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that not all means are equal.

c)

HSD = 2.26*40.66667/4 = 7.21

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