Question

In: Statistics and Probability

An experiment was carried out to study the effect of the percentage of ammonium​ (Factor A)...

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=

Solutions

Expert Solution

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


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