In: Statistics and Probability
An experiment was carried out to study the effect of the percentage of ammonium (Factor A) and the stir rate (Factor B) on the density of the powder produced. The results are in the accompanying table. Complete parts (a) through (e).
At the 0.01 level of significance is there an interaction between the percentage of ammonium and the stir rate?
- Stir_Rate -
Percent_of_Ammonium 100 150
2% 10.83 8.49
2% 14.64 6.84
2% 18.46 9.05
2% 15.86 9.54
30% 12.29 12.97
30% 15.66 15.62
30% 18.26 15.62
30% 15.77 13.81
A.) Determine the value of the test statistic.
FSTAT=
(Round to two decimal places as needed.)
PValue=
B.) at the .01 level of significance, is there an effect due to the percentage of ammonium?
FSTAT=
PValue=
Anova: Two-Factor With Replication | |||||
SUMMARY | STIR100 | STIR150 | Total | ||
2 | |||||
Count | 4 | 4 | 8 | ||
Sum | 59.79 | 33.92 | 93.71 | ||
Average | 14.9475 | 8.48 | 11.71375 | ||
Variance | 10.07289 | 1.3794 | 16.85914 | ||
30 | |||||
Count | 4 | 4 | 8 | ||
Sum | 61.98 | 58.02 | 120 | ||
Average | 15.495 | 14.505 | 15 | ||
Variance | 6.0067 | 1.775233 | 3.615143 | ||
Total | |||||
Count | 8 | 8 | |||
Sum | 121.77 | 91.94 | |||
Average | 15.22125 | 11.4925 | |||
Variance | 6.976898 | 11.72359 | |||
ANOVA | |||||
Source of Variation | SS | df | MS | F | P-value |
FACTOR1 | 43.198 | 1.000 | 43.198 | 8.984 | 0.011 |
FACTOR2 | 55.614 | 1.000 | 55.614 | 11.566 | 0.005 |
Interaction | 30.003 | 1.000 | 30.003 | 6.240 | 0.028 |
Within | 57.703 | 12.000 | 4.809 | ||
Total | 186.5177 | 15 |
FOR INTERACTION F stat = 6.240
p value = 0.028
p value > 0.01 , so not significant
.............
b)
F stat for ammonia = 8.984
p value=0.011
p value > 0.01, not significant
please revert for doubts