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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

    © BrainMass Inc. brainmass.com June 3, 2020, 4:56 pm ad1c9bdddf
    https://brainmass.com/statistics/analysis-of-variance/8705

    Solution Preview

    Answer d: Fisher

    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, ...

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