Question

In an experiment designed to test the output levels of three different treatments, the following results were obtained: SST = 320, SSTR = 130,

*n*_{T} = 19.

Set up the ANOVA table. (Round your values for MSE and
*F* to two decimal places, and your *p*-value to four
decimal places.)

Source of Variation |
Sum of Squares |
Degrees of Freedom |
Mean Square |
F |
p-value |
---|---|---|---|---|---|

Treatments | |||||

Error | |||||

Total |

Test for any significant difference between the mean output levels of the three treatments. Use

*α* = 0.05.

State the null and alternative hypotheses.

*H*_{0}: Not all the population means are
equal.

*H*_{a}: *μ*_{1} =
*μ*_{2} =
*μ*_{3}*H*_{0}: At least two of the
population means are equal.

*H*_{a}: At least two of the population means are
different. *H*_{0}:
*μ*_{1} = *μ*_{2} =
*μ*_{3}

*H*_{a}: Not all the population means are
equal.*H*_{0}: *μ*_{1} ≠
*μ*_{2} ≠ *μ*_{3}

*H*_{a}: *μ*_{1} =
*μ*_{2} =
*μ*_{3}*H*_{0}:
*μ*_{1} = *μ*_{2} =
*μ*_{3}

*H*_{a}: *μ*_{1} ≠
*μ*_{2} ≠ *μ*_{3}

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the *p*-value. (Round your answer to four decimal
places.)

*p*-value =

State your conclusion.

Do not reject *H*_{0}. There is sufficient
evidence to conclude that the means of the three treatments are not
equal.Do not reject *H*_{0}. There is not sufficient
evidence to conclude that the means of the three treatments are not
equal. Reject *H*_{0}. There
is sufficient evidence to conclude that the means of the three
treatments are not equal.Reject *H*_{0}. There is
not sufficient evidence to conclude that the means of the three
treatments are not equal.

Answer #1

*H*_{0}: *μ*_{1} =
*μ*_{2} = *μ*_{3}

*H*_{a}: Not all the population means are equal.

Level of Significance : = 0.05

Anova table :

Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value |

Treatments | 130 | K - 1 = 3-1 = 2 | 65 | 5.4737 | 0.015446 |

Error | 190 | - K = 16 | 11.875 | ||

Total | 320 | - 1 = 18 |

Here, Mean Square = Sum of Squares / Degrees of freedom

F = Mean Square of Treatment / Mean Square of
error

And p-value is obtained from the F tables.

Since p-value < 0.05, we reject *H*_{0} and
conclude that there is sufficient evidence to conclude that the
means of the three treatments are not equal.

Hope this answers your query!

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