Question

A store manager wants to estimate the proportion of customers who spend money in this store. How many customers are required for a random sample to obtain a margin of error of at most 0.075 with 80% confidence

Answer 1

The 73 customers who spend money in this store if  margin of error of at most 0.075 with 80% confidence.

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 p = 0.50 MOE = 0.075

Z = 1.282 at 80% confidence from the Z table.

$\rm 0.075 = (1.282)\sqrt{\dfrac{0.50(1-0.50)}{n}}$

After solving, we get:

n = (0.5)(0.5)/(0.0585)²

n = 73

Thus, the 73 customers who spend money in this store if  margin of error of at most 0.075 with 80% confidence.

Learn more about the Margin of error here:

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