Question

In: Statistics and Probability

To study the effect of temperature on yield in a chemical process, five batches were produced...

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.

Temperature

50°C 60°C 70°C
31 29 25
21 30 30
33 33 30
36 22 32
29 26 33

a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary).

Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value
Treatments
Error
Total

b. Use a  level of significance to test whether the temperature level has an effect on the mean yield of the process.

Calculate the value of the test statistic (to 2 decimals).

Solutions

Expert Solution

a)

Source of Variation Sums of Squares
SS
Degrees of freedom
DF
Mean Squares
MS
F p-value
treatments SSB = 42 k-1 = 4 MSB = 10.5 0.5064 0.7325
error SSW = 207.3333 n-k = 10 MSW = 20.7333
Total SST = 249.3333 n-1 = 14

b)

hence temperature level has no effect on the mean yield of the process.


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