Question

The First National Bank of Wilson has 700 checking account customers. A recent sample of 50 of these customers showed 29 have a Visa card with the bank.
a. What is the margin of error for a 95% confidence interval for the population proportion? (Round your answer to 3 decimal places.)

b. What is the 95% confidence interval for the population proportion?

Answer 1

The margin of error is 0.137 and the confidence interval for the population proportion is (0.443, 0.717).

What is the margin of error(MOE)?

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

$\rm MOE = Z\times \dfrac{s}{\sqrt{n}}$

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            n is the number of samples.

We have:

n = 50, X = 29,

Estimate point p = 29/50 = 0.58

q = 1-p = 1-0.58 = 0.42

Z at 0.05/2 (95% confidence interval) = 1.96

$\rm MOE = 1.96\sqrt{\dfrac{0.58\times0.42}{50}}$

After calculating:

MOE = 0.137

Confidence interval will be: (p - MOE, p+MOE)

= (0.58-0.137, 0.58+0.137)

= (0.443, 0.717)

Thus, the margin of error is 0.137 and the confidence interval for the population proportion is (0.443, 0.717).

Learn more about the Margin of error here:

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