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Answer:
And the F statistic calculated from the mean squares if [tex]F_{calc}[/tex]. And for this case we know that [tex] F_{calc}>F_{critical}[/tex]. So then we can reject the null hypothesis that all the means are equal at a significance level given [tex]\alpha[/tex]. And the best conclusion would be:
reject H0 since there is evidence all the means differ.
Step-by-step explanation:
Previous concepts
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
Solution to the problem
The hypothesis for this case are:
Null hypothesis: [tex]\mu_{A}=\mu_{B}=....=\mu_{k}[/tex]
Alternative hypothesis: Not all the means are equal [tex]\mu_{i}\neq \mu_{j}, i,j=A,B,...,k[/tex]
If we assume that we have [tex]p[/tex] groups and on each group from [tex]j=1,\dots,p[/tex] we have [tex]n_j[/tex] individuals on each group we can define the following formulas of variation:
[tex]SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]
[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex]
[tex]SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]
And we have this property
[tex]SST=SS_{between}+SS_{within}[/tex]
And the F statistic calculated from the mean squares if [tex]F_{calc}[/tex]. And for this case we know that [tex] F_{calc}>F_{critical}[/tex]. So then we can reject the null hypothesis that all the means are equal at a significance level given [tex]\alpha[/tex]. And the best conclusion would be:
reject H0 since there is evidence all the means differ.
In a one-way ANOVA, if the computed F statistic is greater than the critical F value you may eject H0 since there is evidence all the means differ.
What is F-test?
F test is a method used in statistics to determine which models best fits the population from which the sample is derived.
The formula for calculating the F-test statistic = explained variance / unexplained variance
The null hypothesis usually states that the means are the means are the same while the alternative hypothesis states that the means are not the same.
To learn more about the null hypothesis, please check: brainly.com/question/4454077
