Statistics for Management and Economics (Book Only)
Statistics for Management and Economics (Book Only)
11th Edition
ISBN: 9781337296946
Author: Gerald Keller
Publisher: Cengage Learning
Question
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Chapter 14.4, Problem 87E

(a)

To determine

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

(a)

Expert Solution
Check Mark

Explanation of Solution

Table -1 shows the 3 treatments as follows:

Treatment
123
7128
1089
121613
9136
121011

SST (Total) can be calculated as follows:

SS(Total)=j =1k i =1b(xijx¯¯)2=((710)2+(1010.4)2(12+10.4)2+(910.4)2+(1210.4)2+(1210.4)2+(810.4)2+(1310.4)2+(1010.4)2+(810.4)2+(910.4)2+(1310.4)2+(610.4)2+(1110.4)2)=99.6

SST can be calculated as follows:

SST=j =1kb(x¯[T]jx¯¯)2=(5(1010.4)2+(11.810.4)2(9.410.4)2)=15.6

SSB can be calculated as follows:

SSB=j =1kk(x¯[B]jx¯¯)2=(3(910.4)2+(910.4)2+(13.710.4)2+(9.310.4)2+(1110.4)2)=48.3

SSE can be calculated as follows:

SSE=SS(Total)SSTSSB=99.615.648.3=35.7

Thus. The value of SSE is 35.7.

(b)

To determine

Derive SS (Total).

(b)

Expert Solution
Check Mark

Explanation of Solution

SST (Total) can be calculated as follows:

SS(Total)=j =1k i =1b(xijx¯¯)2=((710)2+(1010.4)2(12+10.4)2+(910.4)2+(1210.4)2+(1210.4)2+(810.4)2+(1310.4)2+(1010.4)2+(810.4)2+(910.4)2+(1310.4)2+(610.4)2+(1110.4)2)=99.6

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

SST can be calculated as follows:

SST=j =1kb(x¯[T]jx¯¯)2=(5(1010.4)2+(11.810.4)2(9.410.4)2)=15.6

Thus, the value of SST is 15.6

SSE can be calculated as follows:

SSE=SS(Total)SSTSSB=99.615.6=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
Check Mark

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
Check Mark

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
Check Mark

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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Chapter 14 Solutions

Statistics for Management and Economics (Book Only)

Ch. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.1 - Prob. 16ECh. 14.1 - Prob. 17ECh. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 21ECh. 14.1 - Prob. 22ECh. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.1 - Prob. 25ECh. 14.1 - Prob. 26ECh. 14.1 - Prob. 27ECh. 14.1 - Prob. 28ECh. 14.1 - Prob. 29ECh. 14.1 - Prob. 30ECh. 14.1 - Prob. 31ECh. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Prob. 34ECh. 14.1 - Prob. 35ECh. 14.1 - Prob. 36ECh. 14.1 - Prob. 37ECh. 14.1 - Prob. 38ECh. 14.1 - Prob. 39ECh. 14.1 - Prob. 40ECh. 14.1 - Prob. 41ECh. 14.1 - Prob. 42ECh. 14.1 - Prob. 43ECh. 14.1 - Prob. 44ECh. 14.1 - Prob. 45ECh. 14.1 - Prob. 46ECh. 14.1 - Prob. 47ECh. 14.1 - Prob. 48ECh. 14.1 - Prob. 49ECh. 14.1 - Prob. 50ECh. 14.1 - Prob. 51ECh. 14.1 - Prob. 52ECh. 14.1 - Prob. 53ECh. 14.1 - Prob. 54ECh. 14.1 - Prob. 55ECh. 14.1 - Prob. 56ECh. 14.2 - Prob. 57ECh. 14.2 - Prob. 58ECh. 14.2 - Prob. 59ECh. 14.2 - Prob. 60ECh. 14.2 - Prob. 61ECh. 14.2 - Prob. 62ECh. 14.2 - Prob. 63ECh. 14.2 - Prob. 64ECh. 14.2 - Prob. 65ECh. 14.2 - Prob. 66ECh. 14.2 - Prob. 67ECh. 14.2 - Prob. 68ECh. 14.2 - Prob. 69ECh. 14.2 - Prob. 70ECh. 14.2 - Prob. 71ECh. 14.2 - Prob. 72ECh. 14.2 - Prob. 73ECh. 14.2 - Prob. 74ECh. 14.2 - Prob. 75ECh. 14.2 - Prob. 76ECh. 14.2 - Prob. 77ECh. 14.2 - Prob. 78ECh. 14.2 - Prob. 79ECh. 14.2 - Prob. 80ECh. 14.2 - Prob. 81ECh. 14.2 - Prob. 82ECh. 14.4 - Prob. 83ECh. 14.4 - Prob. 84ECh. 14.4 - Prob. 85ECh. 14.4 - Prob. 86ECh. 14.4 - Prob. 87ECh. 14.4 - Prob. 88ECh. 14.4 - Prob. 89ECh. 14.4 - Prob. 90ECh. 14.4 - Prob. 91ECh. 14.4 - Prob. 92ECh. 14.4 - Prob. 93ECh. 14.4 - Prob. 94ECh. 14.4 - Prob. 95ECh. 14.4 - Prob. 96ECh. 14.4 - Prob. 97ECh. 14.4 - Prob. 98ECh. 14.4 - Prob. 99ECh. 14.5 - Prob. 100ECh. 14.5 - Prob. 101ECh. 14.5 - Prob. 102ECh. 14.5 - Prob. 103ECh. 14.5 - Prob. 104ECh. 14.5 - Prob. 105ECh. 14.5 - Prob. 106ECh. 14.5 - Prob. 107ECh. 14.5 - Prob. 108ECh. 14.5 - Prob. 109ECh. 14.6 - Prob. 110ECh. 14.6 - Prob. 111ECh. 14.6 - Prob. 112ECh. 14.A - Prob. 1ECh. 14.A - Prob. 2ECh. 14.A - Prob. 3ECh. 14.A - Prob. 4ECh. 14.A - Prob. 5ECh. 14.A - Prob. 6ECh. 14.A - Prob. 7ECh. 14.A - Prob. 8ECh. 14.A - Prob. 9ECh. 14.A - Prob. 10ECh. 14.A - Prob. 11ECh. 14.A - Prob. 12ECh. 14.A - Prob. 13ECh. 14.A - Prob. 14ECh. 14.A - Prob. 15ECh. 14.A - Prob. 16ECh. 14.A - Prob. 17ECh. 14.A - Prob. 18ECh. 14.A - Prob. 19ECh. 14.A - Prob. 20ECh. 14.A - Prob. 21ECh. 14.A - Prob. 22ECh. 14.A - Prob. 23ECh. 14.A - Prob. 24ECh. 14.A - Prob. 25ECh. 14.A - Prob. 26ECh. 14.A - Prob. 27ECh. 14.A - Prob. 28ECh. 14.A - Prob. 29ECh. 14.A - Prob. 30ECh. 14.A - Prob. 31ECh. 14.A - Prob. 32ECh. 14.A - Prob. 33ECh. 14.A - Prob. 34ECh. 14.A - Prob. 35ECh. 14.A - Prob. 36ECh. 14.A - Prob. 37ECh. 14.A - Prob. 38ECh. 14.A - Prob. 39ECh. 14.A - Prob. 40ECh. 14.A - Prob. 41ECh. 14.A - Prob. 42ECh. 14 - Prob. 113CECh. 14 - Prob. 114CECh. 14 - Prob. 115CECh. 14 - Prob. 116CECh. 14 - Prob. 117CECh. 14 - Prob. 118CECh. 14 - Prob. 119CECh. 14 - Prob. 120CECh. 14 - Prob. 121CECh. 14 - Prob. 122CECh. 14 - Prob. 123CECh. 14 - Prob. 124CECh. 14 - Prob. 125CECh. 14 - Prob. 126CECh. 14 - Prob. 127CECh. 14 - Prob. 128CECh. 14 - Prob. 129CECh. 14 - Prob. 130CECh. 14 - Prob. 131CECh. 14 - Prob. 132CECh. 14 - Prob. 133CECh. 14 - Prob. 134CECh. 14 - Prob. 135CECh. 14 - Prob. 136CECh. 14 - Prob. 137CECh. 14 - Prob. 138CECh. 14 - Prob. 139CECh. 14 - Prob. 140CECh. 14 - Prob. 141CECh. 14 - Prob. 142CECh. 14 - Prob. 143CECh. 14 - Prob. 144CECh. 14 - Prob. 145CECh. 14 - Prob. 146CE
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