Use the following to solve the questions
A poll of 827 students at Alpha State College found that 61% of those polled preferred a quarter system to a trimester system.
-Estimate a 95% confidence interval for the percentage of students who prefer a quarter system.
A) 59.1% to 62.9%
B) 61% to 65%
C) 50% to 70%
D) 57.6% to 64.4%

Question

Quizplus · Accepted Answer

To estimate a 95% confidence interval, we first need to calculate the standard error of the proportion:

SE = sqrt[(p*(1-p))/n]
SE = sqrt[(0.61*0.39)/827]
SE = 0.022

Next, we can use a normal distribution to calculate the margin of error:

ME = z*SE
ME = 1.96*0.022
ME = 0.043

Finally, we can construct the confidence interval:

CI = p ± ME
CI = 0.61 ± 0.043
CI = (0.567, 0.653)

So the 95% confidence interval for the percentage of students who prefer a quarter system is 57.6% to 64.4%, or choice D.

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