a sample of 150 adults is composed of 100 women and 50 men. estimate the standard error of the proportion for the female population
To estimate the standard error of the proportion for the female population, you need to use the formula:
SE (Standard Error) = √ [(p * (1-p)) / n]
Where:
SE is the standard error
p is the proportion of the group you are interested in (in this case, women)
n is the sample size
In this case, you have a sample of 150 adults, with 100 women and 50 men. So, the proportion of women, p, would be:
p = number of women / total number of adults = 100 / 150 = 2/3
Substituting this information into the formula:
SE = √ [(2/3 * (1-2/3)) / 150]
Simplifying the equation:
SE = √ [(2/3 * 1/3) / 150]
= √ [(2/9) / 150]
= √ (2/9) * 1/√150
≈ 0.087
Therefore, the estimated standard error of the proportion for the female population in this sample is approximately 0.087.