Estimating a Proportion
- Parameter of Interest p
- eg. Percentage of all Americans who have good intuition about experimental design. - Point Estimate p̂
- eg. Percentage of sampled Americans who have good intuition about experimental design.
Building confidence interval
INSTRUCTIONS
1. Check the conditions
2. Construct a confidence interval by estimating the proportion
(Example)
The GSS found that 571 out of 670 (~85%) of Americans answered the question on experimental design correctly. Estimate (using a 95% confidence interval) the proportion of all Americans who have good intuition about experimental design?
The margin of error for the previous confidence interval was 2.7%. If, for a new confidence interval based on a new sample, we wanted to reduce the margin of error to 1% while keeping the confidence level the same, at least how many respondents should we sample?
Calculating the Required Sample Size for Desired ME (Margin of Error)
- If we don’t have any knowledge about the characteristics of the population and there is a previous study that we can rely on for the value of p̂, use that in the calculation of the required sample size
- If not, use p̂ = 0.5
- If you don’t know any better, 50-50 is a good guess
- Gives the most conservative estimate (highest ME) → highest possible sample size
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