1. A company decides to add a new program that prepares randomly selected sales personnel to increase their number of sales per month. The mean number of sales per month for the overall population of sales people at this national company is 25 with a standard deviation of 4. The mean number of sales per month for those who participated in the new program was 29. Compute the effect size of the new sales program.
I'm not sure what you mean by "effect size." However, 29 is one standard deviation above the mean, which involves a difference of about 34%.
To compute the effect size of the new sales program, you will need to use the formula for Cohen's d. Cohen's d is a statistical measure that quantifies the difference between two group means, in standard deviation units. Here is the formula:
Cohen's d = (Mean 1 - Mean 2) / pooled standard deviation
To calculate Cohen's d for the new sales program, follow these steps:
Step 1: Calculate the difference in means:
Mean 1 (sales personnel who participated in the program) = 29
Mean 2 (overall population) = 25
Mean difference = Mean 1 - Mean 2 = 29 - 25 = 4
Step 2: Calculate the pooled standard deviation:
To calculate the pooled standard deviation, you first need to compute the standard deviation for each group:
Standard deviation for the sales personnel who participated in the program:
Standard deviation 1 = 4 (given in the question)
Standard deviation for the overall population:
Standard deviation 2 = 4 (given in the question)
Next, calculate the pooled standard deviation (Spooled):
Spooled = √((n1-1)s1^2 + (n2-1)s2^2) / (n1 + n2 - 2)
where n1 and n2 are the sample sizes, and s1 and s2 are the standard deviations.
Since the sample size of the sales personnel who participated in the program is not given, we cannot calculate the exact Spooled. In this case, we need more information to compute the effect size accurately.