A POOLED SAMPLE:In lots of research contexts, we have multiple studies or polls of the same topic. In those cases, we want to combine the results to draw overall conclusions from all the research that's available.

Two research teams studied the prevalence of dementia in Italian seniors. Ravaglia and coauthors studied 1016 participants and found that 60 of them had dementia. Tognoni and coauthors studied 1600 participants and found that 100 of them had dementia.

Calculate the sample proportion for each study and compute a confidence interval for the population proportion based on each study. Explain your work clearly and what the resulting confidence intervals mean.

What if we combine both studies into a single sample with 2616 participants? How many of those participants have dementia in total? What is the sample proportion for that sample, and what confidence interval does it give us for the population proportion?

Compare the 3 sample proportions. If someone in the future wants to make a policy decision that relies on knowing the percentage of Italian seniors who have dementia, which point estimate and confidence interval should they use, and why?