3. Analysis of variance and the completely randomized design

Telemarketers often follow a pre-written script when interviewing customers. A manager of a major telemarketing company would like to compare the effectiveness of three different sales scripts, Script A, Script B, and Script C.

An investigator performed an experiment in which 32 telemarketing trainees were randomly assigned to three groups: the first consisting of 12 trainees, the second 11 trainees, and the third 9 trainees. Trainees in the first group were trained to market their products using Script A, trainees in the second group were trained to use Script B, and trainees in the third group were trained to use Script C. After training, each trainee's sales amount over a one-week period was recorded.

The sample mean and variance of the sales amounts for each of the three groups are presented in the table below.

Treatment, j	Number of Observations, njj	Sample Mean, x jxj(Thousands of dollars)	Sample Variance, sj2j2(Millions of dollars)
Script A	12	5.69	0.5670
Script B	11	5.43	0.5823
Script C	9	4.78	0.4978

The design of the experiment above is design.

The three treatments define three populations of interest. You will use analysis of variance (ANOVA) to test the hypothesis that the three population means are equal. The results of your analysis will be presented in the ANOVA table below.

ANOVA Table
Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F.	p-value
Treatments
Error
Total

Go through the following steps to complete the ANOVA table.

The overall sample mean for the data is_______ .

The sum of squares due to treatments is______ . The sum of squares due to error is _____ . Thus, the total of sum of squares is ____ . Enter these values in the ANOVA table.

The sum of squares due to treatments has _____ degrees of freedom. The sum of squares due to error has ____ degrees of freedom. The total sum of squares has degrees of freedom. Enter these values in the ANOVA table.

The mean square due to treatments is ____ . The mean square due to error is _____ . So the F test statistic is ____ . Enter these values in the ANOVA table.

Select a Distribution

Use the Distributions tool above to find the p-value of the F test statistic. The p-value is ____ . Enter this value in the ANOVA table.

At a significance level of = 0.01, test the null hypothesis that the population means for all treatments are equal. The null hypothesis is____ . The manager _____ conclude that the different scripts vary in their effectiveness.