In a study to find the proportion of children with asthma in a certain population, we desire a 95% confidence interval with standard error no more than 0.05. Without any prior knowledge of the proportion, what should be our minimum sample size

The minimum sample size should be of 381.

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 zscore that has a pvalue of .

The margin of error is given by:

95% confidence level

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

Without any prior knowledge of the proportion, what should be our minimum sample size

We dont know the population proportion, so we use , which is when the largest sample size is needed. We have to find n for which . So

Rounding up

The minimum sample size should be of 381.

x/3-10=8

x/3=18

x=48