b. Show the proper ANOVA table summarizing your work in part a — Goveia Inc evaluating three possible bonus incentive programs for its sales staff

Goveia Inc. is evaluating three possible bonus incentive programs for its sales staff. During a trial period lasting four months, five sales staff members were randomly assigned to each bonus program. Individual sales figures (in $millions) are shown below:

a. Test the hypothesis that average sales for the three populations represented here are the same. Use a significance level of 5%. (Use Expression 13.2 to compute the within groups sum of squares (SSW) for your analysis.)

b. Show the proper ANOVA table summarizing your work in part a.

SOLUTION

H0: µ1 = µ2 = µ3 (the population means are equal)

HA: The population means are not equal

Sample results:

Program A Program B Program C

a)

Step 1: Compute the Within-Groups Variation.

SSW = (n1-1)s12 + (n2-1)s22 +…+ (nk-1)sk2

= (5-1)1.9392 + (5-1)1.9872 + (5-1) 2.3092

= (4)3.76 + (4)3.95 + (4)5.33 = 52.16

Using Expression 13.2 to compute SSW gives the same result (except small rounding difference):

SSW = (10.4-10.4)2 + (8.4-10.4)2 + (8.8-10.4)2 + (13.2-10.4)2 + (11.2-10.4)2 (Prog A group)

+ (13.3-12)2 + (14.7-12)2 + (11.6-12)2 + (10.5-12)2 + (9.9-12)2 (Prog B group)

+ (10.5-12.4)2 + (11.2-12.4)2 + (16.1-12.4)2 + (11-12.4)2+(13.2-12.4)2 (Prog C group)