![What is the grand mean? [1 pt(s)] Tries 0/3 Submit Answer Calculate the degrees of freedom Salinity Temperature Interaction E](http://img.homeworklib.com/questions/df4b2c50-fd81-11ea-a093-015f43053ceb.png?x-oss-process=image/resize,w_560)
Homework Answers
| replication, n= | 3 | ||||||
| row and coulmn means=Σ x̅i/Σni | |||||||
| A | B | row total means | nj | SSA=nj( x̅j - x̅̅)² | |||
| 1 | 51.95 | 68.94 | 60.445 | 6 | 6*(60.445-75.03)²=1276.3334 | ||
| 2 | 62.19 | 87.75 | 74.97 | 6 | 6*(74.97-75.03)²=0.0216 | ||
| 3 | 78.95 | 100.4 | 89.675 | 6 | 6*(89.675-75.03)²=1286.8562 | ||
| column total means | 64.36333333 | 85.6966667 | 75.03 | ||||
| ni | 9 | 9 | |||||
| SSB=Σni( x̅i - x̅̅)² | 9*(64.3633-75.03)²=1024 | 9*(85.6967-75.03)²=1024 |
==============
.
===================
grand mean , x̅̅ = 75.03
Salinity = dfA = r - 1 = 3-1= 2
Temperature = dfB = c-1 = 2-1= 1
interaction = dfAxB = (r-1)*(c-1) = 2*1=
2
error = dfE = N-rc= 18-3*2=
12
=============
SSbetween=n( x̅ - x̅̅)²=
4666.3254
SSA=Σ nj( x̅j - x̅̅)²=
1276.3334+0.0216+1286.8562= 2563.2112
SSB=Σ ni( x̅i - x̅̅)²= 1024+1024=
2048
SS AxB= SS between-SSA-SSB=
55.1142
SSE=ΣSS= 4678.8777
MSAxB = SSAxB/dfAxB =
55.1142/2= 27.5571
F for interaction = MSAxB/MSE =
0.0707
No, we fail to reject the null hypothesis
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