Calculate the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria: 95% confidence, within 5 percentage points, and a previous estimate is not known.

The minimum number of subjects needed is 385.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the z-score that has a p-value of .

The margin of error is:

95% confidence level

So , z is the value of Z that has a p-value of , so .

95% confidence, within 5 percentage points, and a previous estimate is not known.

The sample size is n for which M = 0.05. We don't know the true proportion, so we use

Then

Rounding up:

The minimum number of subjects needed is 385.