Question

Mrs. Taylor would like to construct a confidence interval for the number of highlighters that are borrowed and not returned in her classroom. At the end of a semester, she loaned 115 highlighters and found that 68% were not returned. What is the confidence interval at a 90%confidence level?


A.
(60.9%,75.1%)

B.
(58%,78%)

C.
(67.3%,68.7%)

D.
(65.4%,71.6%)

Answer 1

The confidence interval at a 90% confidence level is (60.9%,75.1%) if in the end of a semester, she loaned 115 highlighters and found that 68% were not returned option (A) is correct.

What is the margin of error(MOE)?

It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.

The formula for finding the MOE:

$\rm MOE = Z\times{\sqrt \dfrac{p(1-p)}{n}$

Where   Z is the z-score at the confidence interval

            p is the population proportion

            n is the number of samples.

We have p = 68% = 0.68

n = 115

Z score for 90% confidence interval = 1.64

$\rm MOE = 1.64\times{\sqrt \dfrac{0.68(1-0.68)}{115}$

MOE = 0.071

So the confidence interval will be:

= (0.68-0.071, 0.68+0.071)

= (0.609, 0.751)  or

= (60.9%, 75.1%)

Thus, the confidence interval at a 90% confidence level is (60.9%,75.1%) if in the end of a semester, she loaned 115 highlighters and found that 68% were not returned option (A) is correct.

Learn more about the Margin of error here:

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