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# ANOVA

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True or False: When the sum of squares within or sum of squares error (SSE) is added to the sum of squares among (SSA), the result is the total sum of squares (SST).

The technique of analysis of variance was originated in England by ___________ while conducting agricultural experiments.
a. Student
b. Gauss
c. Pascal
d. Fisher

Johnson's Service Center has devised three potential options available to preferred customers who redeem coupons and buy at least 10 gallons of fuel when they stop in. Option A is a flat 3 cents off each gallon. Option B is a combination of 2 cents off plus another \$1 discount on the regular price of a \$5 deluxe car wash. Option C is a \$2 discount on the same \$5 deluxe car wash but no reduction in the fuel purchase. The owner, Harold Johnson, ran each option on three different two-week trial periods and tracked daily sales receipts from those customers who redeemed their coupons. Results are shown in the table below:
Option A
\$453
507
513
521
511
615
601
552
551
505
515
512
476
427

Option B:
\$492
514
536
511
528
678
611
653
596
516
534
543
498
437

Option C:
\$467
525
516
500
435
462
411
674
512
559
624
711
512
416

Harold elected to conduct a one-way ANOVA for his single-factor experiment.

Multiple choice using the information above:
What is the total sum of squares (SST)?
a. 211,049.6
b. 204,880.6
c. 198,711.6
d. 173,512.1

and again using the info above:

What are the values of the F statistic and the critical value at the 0.05 level of significance?
a. 5.325, 19.55
b. 1.653, 5,18
c. 0.937, 3.24
d. 0.605, 3.24

https://brainmass.com/statistics/analysis-of-variance/8705

#### Solution Preview

Let mean of A: <y1>, mean of B = <y2> and of C = <y3>

sum(yi1) = 7259
=> <y1> = 7259/14 = 518.50

sum(yi2) = 7647
=> <y2> = 7647/14 = 546.21

sum(yi3) = 7324
=> <y3> = 7324/14 = 523.14

Grand mean:
<y> = sum(k =1,3) [nk * <yk> ]/sum(k=1,3)[nk]
where, ...

#### Solution Summary

The solution answers the question(s) below.

\$2.19