In: Statistics and Probability
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).
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.