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.
<h3>What is the margin of error(MOE)?</h3>
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}\\](https://tex.z-dn.net/?f=%5Crm%20MOE%20%3D%20Z%5Ctimes%7B%5Csqrt%20%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%5C%5C)
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}\\](https://tex.z-dn.net/?f=%5Crm%20MOE%20%3D%201.64%5Ctimes%7B%5Csqrt%20%5Cdfrac%7B0.68%281-0.68%29%7D%7B115%7D%5C%5C)
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:
brainly.com/question/13990500
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