Please compute \"by hand calculations\" the ANOVA tables for each set of data, u

Question

Please compute "by hand calculations" the ANOVA tables for each set of data, using the summary statistics below. Present the 5 steps of the ANOVA hypothesis test. Please show all work.

Summary Statistics:

6. Porous carbon materials are used commercially in several industrial applications, including gas separation, membrane separation, and fuel cell applications. For the purpose of gas separation, the pore size is impor- tant. To compare the mean pore size of carbon made at temperatures (in OC) of 300, 400, 500, and 600, an experiment uses 5 measurements at each temperature setting (Porous Carbon txt). Is there any difference in the average pore size of carbon made at the different temperatures?

Explanation / Answer

here null hypothesis: all mean values are same

alternate hypothesis: at least two mean are different.

level of significance =0.05 for which critical value =3.0557

from above given data

as F test stat is greater then F critical value we reject that all mean are equal

and we have sufficient evidence at 0.05 level to conclude that at least 2 means are diffierent

i ni Xi S;^2 ni*(Xi-mean)^2 (ni-1)Si^2 1 5 7.43 0.2245 1.445 0.202 2 5 7.24 0.143 0.604 0.082 3 5 6.66 0.083 0.270 0.028 4 5 6.24 0.068 2.129 0.018 mean 6.8925 4.447 0.329 MSG MSE Source of variation SS df MS F P value F crit Between groups 4.447 3 1.482 71.997 0.00000 3.238872 with in groups 0.329 16 0.021 total 4.777 19

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