I want to make a survey with several questions and conclude those results for the whole population. For example, I want to estimate the following questions for my 1 million population : "do you have a dog", "are you single", "is pizza your favorite food", etc... and I want to conclude that (for example) "40% of the whole population has a dog", "44% of the whole population is single", "pizza is the favorite food of 60% of the whole population"
I am looking at the sample size needed for surveys on this page, and it says the formula for estimating the sample size of a survey is:
$$Sample\;size = \frac{\frac{z^2 \;\times \;p(1-p)}{e^2}}{1 + (\frac{z^2 \; \times \; p(1-p)}{e^2N})}$$
where
- $e$ is the margin of error
- $N$ is the population size.
- $p$ is the proportion
For the online calculation, one gives as input the confidence level, the whole population size, and the margin of error. For a confidence interval of $95\%$ and a margin of error of $3\%$, for the 1 million population, it gives a sample size of 1066. However, what is the proportion here? How can I interpret it since I did not give any value for input?
Edit: If I survey >1066 persons (among the whole population), can I make several conclusions about the population? Or is this sample only able to estimate ONE thing? Can I use this sample to estimate several proportions, or can I only estimate one proportion? Also, are proportions used only for Yes/No questions?
If from my sample of 1066, half of them (proportion of 0.5) have a dog, can I automatically say that the true proportion of the population is in the 95% confidence interval = $]0.5-0.03,0.05+0.03[=]0.47,0.53[$ ? Or do I need to some calculations for the confidence interval?