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# ANOVA Hypotheses Testing

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The manufacturer of batteries is designing a battery to be used in a device that will be subjected to extremes in temperature. The company has a choice of 3 materials to use in the manufacturing process. An experiment is designed to study the life of the battery when it is made from materials A, B, and C and is exposed to temperatures of 15,70, and 125 degrees F. For each combination of material and temperature 4 batteries are tested. The lifetime in hours of the batteries are shown below:
Temperatures
Material A
15°F
130,155,74,180

70°F
34,40,80,75

125°F
20,70,82,58

Material B
15°F
150,188,159,126

70°F
126,122,106,115

125°F
25,70,58,45

Material C
15°F
138,110,168,160

70°F
174,120,150,139

125°F
96,104,82,60

a. Calculate the average life for each of the 3 materials.
b. Calculate the average life for each of the 3 temperatures.
c. Calculate the average life for each of the 9 treatment groups.
d. Plot the 9 treatment means on a graph with temperature factor on the x-axis, and the life of the battery in hours on the y-axis. Use a different color for each of the 3 materials and connect the averages for those of the same material. What do you speculate about the interaction effect based on the graph?
e. Confirm your suspicions by doing a two-way ANOVA and testing to see if there is a significant interaction effect.
f. What material do you recommend to this manufacturer and why?

https://brainmass.com/statistics/analysis-of-variance/anova-hypotheses-testing-8509

#### Solution Preview

a.)
avg life for material A:
<A> = {(130+155+74+180)+(34+40+80+75)+(20+70+82+58)}/12
=> <A> = 83.17 ~ 83 hrs --Answer
avg life for material B:
b = ((150+188+159+126)+(126+122+106+115)+(25+70+58+45))/12
=> b = 107.5 ~ 108 hrs --Answer
avg life for material C:
<C> = ((138+110+168+160)+(174+120+150+139)+(96+104+82+60))/12
=> <C> = 125.08 ~ 125 hrs --Answer

b.)
avg life for temperature 15 deg.F:
<15> = ((130+155+74+180) + (150+188+159+126) +(138+110+168+160))/12
=> <15> = 144.83 ~ 145 hrs --Answer
<70> = ((34+40+80+75) + ...

#### Solution Summary

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