If you wanted to be 98 percent confident that your data was going to be reflective of the entire population of 500000, how many would be your respondents?

To determine the sample size needed for a 98% confidence level for a population of 500,000, you can use the formula for sample size calculation:

n = Z^2 * p(1-p) / E^2

Where:

• n is the sample size
• Z is the Z-value (which is 2.33 for a 98% confidence level)
• p is the estimated proportion of the population which has the attribute in question (if you don't have a specific estimate, you can use 0.5 to maximize the sample size)
• E is the margin of error (which is typically set at 0.05 for a 95% confidence level)

Let's calculate:

n = 2.33^2 * 0.5(1-0.5) / 0.05^2 n = 5.4289 * 0.25 / 0.0025 n = 1.357225 / 0.0025 n = 542.89

So, you would need a sample size of approximately 543 respondents to be 98% confident that your data is reflective of the entire population of 500,000. Please note that this is a simplified calculation and actual sample size may vary depending on the variability of the population and the precision required.