Derive SST, SSB, SSE, and SS (Total).

Question

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Answer 1

Question

Chapter 14.4, Problem 87E

(a)

To determine

Derive SST, SSB, SSE, and SS (Total).

(a)

Expert Solution

Explanation of Solution

Table -1 shows the 3 treatments as follows:

Treatment
1	2	3
7	12	8
10	8	9
12	16	13
9	13	6
12	10	11

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

SSB can be calculated as follows:

SSB=∑j =1kk(x¯[B]j−x¯¯)2=(3(9−10.4)2+(9−10.4)2+(13.7−10.4)2+(9.3−10.4)2+(11−10.4)2)=48.3

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6−48.3=35.7

Thus. The value of SSE is 35.7.

(b)

To determine

Derive SS (Total).

(b)

Expert Solution

Explanation of Solution

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

Thus, the value of SS (Total) is 99.6.

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

Thus, the value of SST is 15.6

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6=84

Thus. The value of SSE is 88.

(c)

To determine

Explain the way in which SS (Total) remains the same for both experimental designs.

(c)

Expert Solution

Explanation of Solution

From the estimation result, the variation between all the data is the same for both designs.

(d)

To determine

Explain the way in which SST remains the same for both experimental designs.

(d)

Expert Solution

Explanation of Solution

From the estimation result, the variation between treatments is the same for both designs.

(e)

To determine

Explain the way in which SSB+SSE is a part that is equal to SSE.

(e)

Expert Solution

Explanation of Solution

SSB + SSE is a part that is equal to SSE because the randomized block designs divide the sum of squares for error in the one – way analysis of variance into two parts.

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Answer 2

Question

Chapter 14.4, Problem 87E

(a)

To determine

Derive SST, SSB, SSE, and SS (Total).

(a)

Expert Solution

Explanation of Solution

Table -1 shows the 3 treatments as follows:

Treatment
1	2	3
7	12	8
10	8	9
12	16	13
9	13	6
12	10	11

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

SSB can be calculated as follows:

SSB=∑j =1kk(x¯[B]j−x¯¯)2=(3(9−10.4)2+(9−10.4)2+(13.7−10.4)2+(9.3−10.4)2+(11−10.4)2)=48.3

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6−48.3=35.7

Thus. The value of SSE is 35.7.

(b)

To determine

Derive SS (Total).

(b)

Expert Solution

Explanation of Solution

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

Thus, the value of SS (Total) is 99.6.

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

Thus, the value of SST is 15.6

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6=84

Thus. The value of SSE is 88.

(c)

To determine

Explain the way in which SS (Total) remains the same for both experimental designs.

(c)

Expert Solution

Explanation of Solution

From the estimation result, the variation between all the data is the same for both designs.

(d)

To determine

Explain the way in which SST remains the same for both experimental designs.

(d)

Expert Solution

Explanation of Solution

From the estimation result, the variation between treatments is the same for both designs.

(e)

To determine

Explain the way in which SSB+SSE is a part that is equal to SSE.

(e)

Expert Solution

Explanation of Solution

SSB + SSE is a part that is equal to SSE because the randomized block designs divide the sum of squares for error in the one – way analysis of variance into two parts.

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Answer 3

Question

Chapter 14.4, Problem 87E

(a)

To determine

Derive SST, SSB, SSE, and SS (Total).

(a)

Expert Solution

Explanation of Solution

Table -1 shows the 3 treatments as follows:

Treatment
1	2	3
7	12	8
10	8	9
12	16	13
9	13	6
12	10	11

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

SSB can be calculated as follows:

SSB=∑j =1kk(x¯[B]j−x¯¯)2=(3(9−10.4)2+(9−10.4)2+(13.7−10.4)2+(9.3−10.4)2+(11−10.4)2)=48.3

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6−48.3=35.7

Thus. The value of SSE is 35.7.

(b)

To determine

Derive SS (Total).

(b)

Expert Solution

Explanation of Solution

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

Thus, the value of SS (Total) is 99.6.

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

Thus, the value of SST is 15.6

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6=84

Thus. The value of SSE is 88.

(c)

To determine

Explain the way in which SS (Total) remains the same for both experimental designs.

(c)

Expert Solution

Explanation of Solution

From the estimation result, the variation between all the data is the same for both designs.

(d)

To determine

Explain the way in which SST remains the same for both experimental designs.

(d)

Expert Solution

Explanation of Solution

From the estimation result, the variation between treatments is the same for both designs.

(e)

To determine

Explain the way in which SSB+SSE is a part that is equal to SSE.

(e)

Expert Solution

Explanation of Solution

SSB + SSE is a part that is equal to SSE because the randomized block designs divide the sum of squares for error in the one – way analysis of variance into two parts.

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Answer 4

Question

Chapter 14.4, Problem 87E

(a)

To determine

Derive SST, SSB, SSE, and SS (Total).

(a)

Expert Solution

Explanation of Solution

Table -1 shows the 3 treatments as follows:

Treatment
1	2	3
7	12	8
10	8	9
12	16	13
9	13	6
12	10	11

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

SSB can be calculated as follows:

SSB=∑j =1kk(x¯[B]j−x¯¯)2=(3(9−10.4)2+(9−10.4)2+(13.7−10.4)2+(9.3−10.4)2+(11−10.4)2)=48.3

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6−48.3=35.7

Thus. The value of SSE is 35.7.

(b)

To determine

Derive SS (Total).

(b)

Expert Solution

Explanation of Solution

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

Thus, the value of SS (Total) is 99.6.

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

Thus, the value of SST is 15.6

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6=84

Thus. The value of SSE is 88.

(c)

To determine

Explain the way in which SS (Total) remains the same for both experimental designs.

(c)

Expert Solution

Explanation of Solution

From the estimation result, the variation between all the data is the same for both designs.

(d)

To determine

Explain the way in which SST remains the same for both experimental designs.

(d)

Expert Solution

Explanation of Solution

From the estimation result, the variation between treatments is the same for both designs.

(e)

To determine

Explain the way in which SSB+SSE is a part that is equal to SSE.

(e)

Expert Solution

Explanation of Solution

SSB + SSE is a part that is equal to SSE because the randomized block designs divide the sum of squares for error in the one – way analysis of variance into two parts.

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Answer 5

Chapter 14.4, Problem 87E

(a)

To determine

Derive SST, SSB, SSE, and SS (Total).

(a)

Expert Solution

Explanation of Solution

Table -1 shows the 3 treatments as follows:

Treatment
1	2	3
7	12	8
10	8	9
12	16	13
9	13	6
12	10	11

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

SSB can be calculated as follows:

SSB=∑j =1kk(x¯[B]j−x¯¯)2=(3(9−10.4)2+(9−10.4)2+(13.7−10.4)2+(9.3−10.4)2+(11−10.4)2)=48.3

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6−48.3=35.7

Thus. The value of SSE is 35.7.

(b)

To determine

Derive SS (Total).

(b)

Expert Solution

Explanation of Solution

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

Thus, the value of SS (Total) is 99.6.

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

Thus, the value of SST is 15.6

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6=84

Thus. The value of SSE is 88.

(c)

To determine

Explain the way in which SS (Total) remains the same for both experimental designs.

(c)

Expert Solution

Explanation of Solution

From the estimation result, the variation between all the data is the same for both designs.

(d)

To determine

Explain the way in which SST remains the same for both experimental designs.

(d)

Expert Solution

Explanation of Solution

From the estimation result, the variation between treatments is the same for both designs.

(e)

To determine

Explain the way in which SSB+SSE is a part that is equal to SSE.

(e)

Expert Solution

Explanation of Solution

SSB + SSE is a part that is equal to SSE because the randomized block designs divide the sum of squares for error in the one – way analysis of variance into two parts.

Answer 6

Chapter 14.4, Problem 87E

(a)

To determine

Derive SST, SSB, SSE, and SS (Total).

(a)

Expert Solution

Explanation of Solution

Table -1 shows the 3 treatments as follows:

Treatment
1	2	3
7	12	8
10	8	9
12	16	13
9	13	6
12	10	11

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

SSB can be calculated as follows:

SSB=∑j =1kk(x¯[B]j−x¯¯)2=(3(9−10.4)2+(9−10.4)2+(13.7−10.4)2+(9.3−10.4)2+(11−10.4)2)=48.3

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6−48.3=35.7

Thus. The value of SSE is 35.7.

Answer 7

Chapter 14.4, Problem 87E

(a)

To determine

Derive SST, SSB, SSE, and SS (Total).

Answer 8

(a)

Expert Solution

Explanation of Solution

Table -1 shows the 3 treatments as follows:

Treatment
1	2	3
7	12	8
10	8	9
12	16	13
9	13	6
12	10	11

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

SSB can be calculated as follows:

SSB=∑j =1kk(x¯[B]j−x¯¯)2=(3(9−10.4)2+(9−10.4)2+(13.7−10.4)2+(9.3−10.4)2+(11−10.4)2)=48.3

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6−48.3=35.7

Thus. The value of SSE is 35.7.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

(b)

To determine

Derive SS (Total).

(b)

Expert Solution

Explanation of Solution

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

Thus, the value of SS (Total) is 99.6.

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

Thus, the value of SST is 15.6

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6=84

Thus. The value of SSE is 88.

Answer 13

(b)

To determine

Derive SS (Total).

Answer 14

(b)

Expert Solution

Explanation of Solution

SST (Total) can be calculated as follows:

SS(Total)=∑j =1k∑ i =1b(xij−x¯¯)2=((7−10)2+(10−10.4)2(12+10.4)2+(9−10.4)2+(12−10.4)2+(12−10.4)2+(8−10.4)2+(13−10.4)2+(10−10.4)2+(8−10.4)2+(9−10.4)2+(13−10.4)2+(6−10.4)2+(11−10.4)2)=99.6

Thus, the value of SS (Total) is 99.6.

SST can be calculated as follows:

SST=∑j =1kb(x¯[T]j−x¯¯)2=(5(10−10.4)2+(11.8−10.4)2(9.4−10.4)2)=15.6

Thus, the value of SST is 15.6

SSE can be calculated as follows:

SSE=SS(Total)−SST−SSB=99.6−15.6=84

Thus. The value of SSE is 88.

Answer 15

(b)

Expert Solution

Answer 16

(b)

Expert Solution

Answer 17

Expert Solution

Answer 18

(c)

To determine

Explain the way in which SS (Total) remains the same for both experimental designs.

(c)

Expert Solution

Explanation of Solution

From the estimation result, the variation between all the data is the same for both designs.

Answer 19

(c)

To determine

Explain the way in which SS (Total) remains the same for both experimental designs.

Answer 20

(c)

Expert Solution

Explanation of Solution

From the estimation result, the variation between all the data is the same for both designs.

Answer 21

(c)

Expert Solution

Answer 22

(c)

Expert Solution

Answer 23

Expert Solution

Answer 24

(d)

To determine

Explain the way in which SST remains the same for both experimental designs.

(d)

Expert Solution

Explanation of Solution

From the estimation result, the variation between treatments is the same for both designs.

Answer 25

(d)

To determine

Explain the way in which SST remains the same for both experimental designs.

Answer 26

(d)

Expert Solution

Explanation of Solution

From the estimation result, the variation between treatments is the same for both designs.

Answer 27

(d)

Expert Solution

Answer 28

(d)

Expert Solution

Answer 29

Expert Solution

Answer 30

(e)

To determine

Explain the way in which SSB+SSE is a part that is equal to SSE.

(e)

Expert Solution

Explanation of Solution

SSB + SSE is a part that is equal to SSE because the randomized block designs divide the sum of squares for error in the one – way analysis of variance into two parts.

Answer 31

(e)

To determine

Explain the way in which SSB+SSE is a part that is equal to SSE.

Answer 32

(e)

Expert Solution

Explanation of Solution

SSB + SSE is a part that is equal to SSE because the randomized block designs divide the sum of squares for error in the one – way analysis of variance into two parts.