Question: Hypothesis testing with ANOVA #2 - The p-value approach

Telemarketers often follow a prewritten script when interviewing customers. A manager of a major telemarketing company would like to comp-are the effectiveness of three different sales scripts, Script A, Script B, and Script C. An investigator performs an experiment in which 40 telemarketing trainees are randomly assigned to three groups: the first consisting of 12 trainees, the second 13 trainees, and the third 15 trainees. Trainees in the first group are trained to market their products using Script A, trainees in the second group are trained to use Script B, and trainees in the third group are trained to use Script C. After training, each trainee’s sales total over a one-week period is recorded.

The sample size, total, mean, and \(\sum{x_{i}^{2}}\) for the sales totals for each of the three groups are presented in the table below.

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

Go through the following steps to complete the ANOVA table.

1. Enter the value of the sum of squares due to factor, the sum of squares due to error, and the total sum of squares in the ANOVA table.
2. Enter all of the degrees of freedom in the ANOVA table.
3. Enter the values of the mean square for factor, the mean square for error, and the F-test statistic in the ANOVA table.
4. Use the Distributions tool above to find the p-value for the F-test statistic. Enter this p-value in the ANOVA table. At a significance level of 0: = 0.05, the investigator tests the null hypothesis that the population means for all factor levels are equal. The null hypothesis is ; therefore the manager of the telemarketing company conclude that the different scripts vary in their effectiveness.

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