calculate a modest- estimate of sample size that would be appropriate at 90% confidence of estimating 3 proportions of people experiencing stress with plus minus 0.03.
To calculate the sample size needed for estimating multiple proportions with a specific level of confidence and margin of error, we can use a formula known as the Sample Size Formula for estimating proportions.
The formula for calculating the sample size is:
n = (Z^2 * P * (1-P))/E^2
Where:
n = required sample size
Z = Z-value for the desired confidence level (in this case, 90% confidence)
P = estimated proportion of the population (proportion of people experiencing stress)
E = margin of error (plus/minus 0.03)
To calculate the Z-value for 90% confidence, we can use a standard normal distribution table. The Z-value for 90% confidence is approximately 1.645.
Let's assume you want to estimate three proportions: p1, p2, and p3, each representing the proportion of people experiencing stress in three different groups.
To calculate the sample size for each proportion, you will need to estimate the population proportions or use a pilot study to get an idea of the proportions. Let's call these estimated proportions p1̂, p2̂, and p3̂.
Now, substitute the values into the formula for each proportion:
n1 = (Z^2 * p1̂ * (1-p1̂))/E^2
n2 = (Z^2 * p2̂ * (1-p2̂))/E^2
n3 = (Z^2 * p3̂ * (1-p3̂))/E^2
After calculating the required sample size for each proportion, you can add them together to get your estimated sample size for all three proportions.