Use the given data to find the minimum sample size required to estimate the population proportion. a. Margin of error: 0.004: confidence level: 95% p and q unknown
b. Margin of error: 0.009, confidence level: 99%; p and q unknown
c. Margin of error: 0.01; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 52%.

a. The minimum sample size required is of 60,025.

b. The minimum sample size required is of 20,465.

c. The minimum sample size required is 9,589.

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:

Question a:

95% confidence level

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

p and q unknown means that we use , which is when the largest sample size is needed.

Margin of error: 0.004

We have to find n for which M = 0.004. So

The minimum sample size required is of 60,025.

b. Margin of error: 0.009, confidence level: 99%; p and q unknown

99% confidence level

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

Margin of error: 0.009

We have to find n for which M = 0.009. So

Rounding up:

The minimum sample size required is of 20,465.

c. Margin of error: 0.01; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 52%.

Here we have .

The minimum sample size is n for which M = 0.01. So

Rounding up:

The minimum sample size required is 9,589.

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values