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spayn [35]
2 years ago
6

Compare the mathematical meaning of the word limit with its commonly used meanings. For the word’s mathematical meaning, think o

f how it was defined and used in this unit. For the word’s common meanings, start with the usage of limit as it is used in everyday speech, but also consider idioms and expressions that leverage the common meaning of limit in creative conversation
Mathematics
1 answer:
vredina [299]2 years ago
4 0
This is<span> not the exact, precise </span>definition<span> of a </span>limit. If you would like to see the more precise and mathematical definition<span> of a </span>limit<span> you should check out the The </span>Definition<span> of a </span>Limit<span> section at the end of this chapter. The </span>definition<span> given above </span>is<span> more of a “working” </span>definition<span>.</span>
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Answer:

F = \frac{MSR}{MSE} =\frac{45.89}{6.27}=7.32

So then the best option is:

a. 7.32

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"  

If we assume that we have 3 groups and on each group from j=1,\dots,10 we have 10 individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2  

SS_{between=Treatment}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2  

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2  

And we have this property  

SST=SS_{between}+SS_{within}

Where SST represent the total sum of squares.  

The degrees of freedom for the numerator on this case is given by df_{num}=k-1=3-1=2 where k =3 represent the number of groups.  

The degrees of freedom for the denominator on this case is given by df_{den}=df_{between}=N-K=30-3=27.  

And the total degrees of freedom would be df=N-1=30 -1 =29  

From the info given we know that MSR=\frac{SSR}{2}=45.89

And MSE=\frac{SSE}{27}=6.27

From definition the F statisitc is defined as:

F = \frac{MSR}{MSE} =\frac{45.89}{6.27}=7.32

So then the best option is:

a. 7.32

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