Essentials Of Business Statistics 5th Edition By Bruce Bowerman – Test Bank

CHAPTER 11—Experimental Design and Analysis of Variance

§11.2 Concepts

11.1   The response variableis the variable of interest in an experiment; the dependent variable.

The factoris the independent variables in a designed experiment.  (We wish to study how the factor(s) affect the response variable.)

Thetreatmentsarevalues (or levels) of a factor (or combination of factors.)

The experimental unitsare the entities to which the treatments are assigned.

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11.2    In order to validly use the one-way ANOVA formulas, The following assumptions must be met: Constant variance, normality, and independence (see page 409 for more details)

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11.3    The between treatment variability is obtained by measuring the variability of the sample treatment means, while the within treatment variability is obtained by measuring the variability within each of the sampletreatments.

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11.4    If the one-way ANOVA F test leads us to conclude that at least two of the treatment means differ, then we wish to investigate which of the treatment means differ and we wish to estimate the size of the differences.

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§11.2 Methods and Applications

11.5    a.   H₀: μ_B=μ_M= μ_T
H_a: at least two means differ

α = .05
p = 3,
n =n_B +n_M+ n_T = 6 + 6 + 6 = 18

numeratordf = p – 1 = 3-1 = 2
denominator df = n – p = 18 – 3 = 15
F_.05,2,15 = 3.68

From the Minitab output: F = 184.57, p-value = .000

Since F = 184.57 > 3.68 we reject H₀.
Conclude that shelf location affects sales.

55. From the Minitab output: x̅_B = 55.8x̅_M = 77.2     x̅_T = 51.5     MSE = 6.16

m =n_B =n_M= n_T = 6

                 first value = p = 3
second value = n – p = 18 – 3 = 15
Tukeyq_{(α/2),p,(n-p)} = q_.05,3,15 = 3.67

1.   Bottom–Middle:
   Point estimate for μ_B–μ_M = x̅_B – x̅_B = 55.8 – 77.2 = –21.4
   Confidence interval:
   =  = [–21.4 ± 3.7186]
   = [-25.1186, -17.6814]
2. Bottom–Top:
   Point estimate for μ_B–μ_T = x̅_B – x̅_T = 4.3
   Confidence interval: [0.5814, 8.0186]
3. Middle–Top:
   Point estimate for μ_M–μ_T = x̅_M – x̅_T = 25.7
   Confidence interval:[21.9814, 29.4186]

The Middle display height maximizes the sales.

2. t_.025,15 = 2.131

                 Bottom:  =  = [55.8 ±2.1592] = [53.6408, 57.9592]

Middle: [75.0408, 79.3592]

Top: [49.3408, 53.6592]

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11.6    a.   F = 30.11, p-value =.000

Reject H₀.  Display panels are different.

4. AB: 4.0, [–1.69, 9.69]

AC: –11.25, [–16.94, –5.56]

BC: –15.25, [–20.94,–9.56]

Appears that B minimizes the time

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11.7    a.   F = 43.36, p-value = .000

Reject H₀. The bottle design does have an impact on sales.

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11.8    F = 16.42, p-value = less than .001

           Reject H₀. Conclude differences exist.

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11.9    Tukey q_.05 = 4.05, MSE = 606.15, m = 5

Divot – Alpha: (336.6 – 253.6) ± 44.59: [38.41, 127.59]

Divot – Century: (336.6 – 241.8) ± 44.59: [50.21, 139.39]

Divot – Best: (336.6 – 306.4) ± 44.59: [–14.39, 74.79]

Century – Alpha: (241.8 – 253.6) ± 44.59: [–56.39, 32.79]

Century – Best: (241.8 – 306.4) ± 44.59: [–109.19, –20.01]

Best – Alpha: (306.4 – 253.6) ± 44.59: [8.21,97.39]

Best and Divot appear to be the most durable

           t_.025 = 2.120, MSE = 606.16, n = 5

Divot: 336.6 ±23.34 [313.26, 359.94]

Best: 306.4 ±23.34 [283.06, 329.74]

Alpha: 253.6 ±23.34 = [230.26, 276.94]

Century: 241.8 ± 23.34[218.46, 265.14]

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§11.3Concepts

11.10  We would use the randomized block design when there are differences between the experimental units that are concealing any true differences between the treatments.

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