Calculate p ̅.
x1 20
n1 50
x2 55
n2 100
To calculate the sample mean difference (p̅), you will need to find the difference in proportions between two groups.
The formula to calculate the sample mean difference is:
p̅ = (x1/n1) - (x2/n2)
Where:
x1 = number of favorable outcomes in the first group
n1 = total number of observations in the first group
x2 = number of favorable outcomes in the second group
n2 = total number of observations in the second group
In this case, x1 is 20, n1 is 50, x2 is 55, and n2 is 100. Plugging these values into the formula, you can calculate p̅ as follows:
p̅ = (20/50) - (55/100)
First, simplify each division:
p̅ = 0.4 - 0.55
Next, subtract the values:
p̅ = -0.15
Therefore, the sample mean difference (p̅) is -0.15.