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masha68 [24]
2 years ago
12

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?
Mathematics
1 answer:
attashe74 [19]2 years ago
3 0

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

<h3>What is the margin of error(MOE)?</h3>

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:

brainly.com/question/13990500

#SPJ1

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