A university wants to increase its retention rate of 4% for graduating students from the previous year.After implementing several new programs during the last two years,in 2014 the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%.Create a 95% confidence interval for the proportion of students (in 2014)who had been retained.
A)Based on the data,we are 95% confident the proportion of students in 2004 who had been retained is between 1.95% and 7.05%.
B)Based on the data,we are 95% confident the proportion of students in 2004 who had been retained is between 4% and 6%.
C)Based on the data,we are 95% confident the proportion of students in 2004 who had been retained is between 1.16% and 8.84%.
D)Based on the data,we are 95% confident the proportion of students in 2004 who had been retained is between 2.72% and 7.28%.
E)Based on the data,we are 95% confident the proportion of students in 2004 who had been retained is between 1.95% and 6.05%.

Question

Quizplus · Accepted Answer

The 95% confidence interval for the proportion of students who had been retained is calculated using the formula (p̂ ± z*√((p̂(1-p̂))/n)), where p̂ is the sample proportion, z* is the z-value for the 95% confidence level (1.96), and n is the sample size. Substituting the given values, we get (0.05 ± 1.96*√((0.05(0.95))/352)), which simplifies to (0.0272, 0.0728). Therefore, we can say with 95% confidence that the proportion of students who had been retained in 2014 is between 2.72% and 7.28%. The answer is D.

A University Wants to Increase Its Retention Rate of 4