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    Two-way analysis of variance (ANOVA) with replication

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    An experiment is conducted to study the effects of two sales approaches-high-pressure (H) and low-pressure (L)-and to study the effects of two sales pitches (1 and 2) on the weekly sales of a product. The data in Table (1) below are obtained by using a completely randomized design, and Figure (2) gives the Excel output of a two-way ANOVA of the sales experiment data.

    a Perform graphical analysis to check for interaction between sales pressure and sales pitch.

    b Test for interaction by setting a = .05.

    c Test for differences in the effects of the levels of sales pressure by setting a _ .05. That is, test the significance of sales pressure effects with a = .05.

    d Calculate and interpret a 95 percent individual confidence interval for
    uH - uL

    e Test for differences in the effects of the levels of sales pitch by setting a = .05. That is, test the significance of sales pitch effects with a = .05.

    f Calculate and interpret a 95 percent individual confidence interval for
    u1 - u2.

    g Calculate a 95 percent (individual) confidence interval for mean sales when using high sales pressure and sales pitch 1. Interpret this interval.

    (1) Results of the Sales Approach Experiment

    Sales Pressure
    1 2
    H
    32 32
    29 30
    30 28

    L 28 25
    25 24
    23 23

    (2) Excel Output of a Two-Way ANOVA of the
    Sales Approach Data

    Anova: Two-Factor with Replication

    SUMMARY One Two Total
    H
    Count 3 3 6
    Sum 91 90 181
    Average 30.33333 30 30.16667p
    Variance 2.333333 4 2.566667

    L
    Count 3 3 6
    Sum 76 72 148
    Average 25.33333 24 24.66667q
    Variance 6.333333 1 3.466667

    Total
    Count 6 6
    Sum 167 162
    Average 27.83333r 27s
    Variance 10.96667 12.8

    ANOVA
    Source of
    Variation SS df MS F p-Value F Crit
    Pressure 90.75 (a) 1 90.75 (f) 26.56098 (j) 0.00087 (k) 5.317645
    Pitch 2.083333 (b) 1 2.083333 (g) 0.609756 (l) 0.457362 (m) 5.317645
    Interaction 0.75 (c) 1 0.75 (h) 0.219512 (n) 0.651913 (o) 5.317645
    Within 27.33333 (d) 8 3.416667(i)
    Total 120.9167 (e) 11

    (a) SS(1)
    (b) SS(2)
    (c) SS(int)
    (d) SSE
    (e) SSTO
    (f) MS(1)
    (g) MS(2)
    (h) MS(int)
    (i) MSE
    (j) F(1)
    (k) p-value for F(1)
    (l) F(2)
    (m) p-value for F(2)
    (n) F(int)
    (o) p-value for F(int)

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    https://brainmass.com/statistics/analysis-of-variance/two-way-analysis-of-variance-anova-with-replication-23529

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    In this solution we analyze and interpret a two-way analysis of variance (ANOVA). We show a graphical ...

    Solution Summary

    In this solution we analyze and interpret a two-way analysis of variance (ANOVA). We show a graphical analysis to check for interaction along with a formal test for interaction. We calculate a confidence interval for the difference in means (main effects) and confidence interval for a cell mean.

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