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 popualtion 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
Here is one formula for effect size:
Cohen’s d = the difference between two means divided by a standard deviation.
I'll let you take it from here.
To compute the effect size of the new sales program, we can use Cohen's d formula. Cohen's d is a measure that quantifies the difference between two groups by comparing their means and standard deviations.
The formula for calculating Cohen's d is:
Cohen's d = (Mean difference between groups) / (Pooled standard deviation)
Let's break down the steps to calculate the effect size of the new sales program:
Step 1: Calculate the mean difference between the two groups:
Mean difference = Mean of the program participants - Mean of the overall population
Mean difference = 29 - 25
Mean difference = 4
Step 2: Calculate the pooled standard deviation:
Pooled standard deviation can be calculated using the formula:
Pooled Standard Deviation = √((n1-1) * (sd1^2) + (n2-1) * (sd2^2)) / (n1 + n2 - 2)
Where:
n1 = Sample size of the program participants
n2 = Sample size of the overall population
sd1 = Standard deviation of the program participants
sd2 = Standard deviation of the overall population
Given:
n1 is not provided
n2 is assumed as the overall population sample size
Mean number of sales per month for the overall population = 25
Standard deviation of the overall population = 4
We'll proceed with the assumption that the sample sizes of the two groups are equal for calculation purposes. So n1 = n2.
Step 3: Substitute the values in the formula and calculate:
Pooled Standard Deviation = √((n1-1) * (sd1^2) + (n2-1) * (sd2^2)) / (n1 + n2 - 2)
Pooled Standard Deviation = √((n1-1) * (4^2) + (n2-1) * (4^2)) / (n1 + n2 - 2)
Step 4: Calculate Cohen's d:
Cohen's d = Mean difference / Pooled Standard Deviation
Substitute the values and calculate the effect size:
Cohen's d = 4 / Pooled Standard Deviation
Since the sample sizes (n1 and n2) are not provided, it's challenging to calculate the exact effect size without additional information. However, you can still calculate Cohen's d if you have the sample sizes for both groups and substitute them into the formula.