Assume that you wish to estimate a population proportion, p. For the given margin of error and confidence level, determine the sample size required: A researcher wants to determine what proportion of adults in one town regularly buy organic food. Obtain a sample size that will ensure a margin of error of at most 0.04 for a 90% confidence interval. In previous years, the proportion has been 0.16 .

The sample size required is 228.

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 of:

90% confidence level

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

In previous years, the proportion has been 0.16.

This means that

Obtain a sample size that will ensure a margin of error of at most 0.04 for a 90% confidence interval.

This is n for which M = 0.04. So

Rounding up:

The sample size required is 228.