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 2004 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 2004)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

In order to create a confidence interval for the proportion of students retained, we will use the formula:

proportion ± z*sqrt(proportion*(1-proportion)/n)

Here, proportion = 0.05 (the sample proportion), n = 352, and we will use a z-value of 1.96 (since we want a 95% confidence interval).

Plugging in these values, we get:

0.05 ± 1.96*sqrt(0.05*(1-0.05)/352)
= 0.05 ± 0.022
= (0.028, 0.072)

Therefore, we can say with 95% confidence that the proportion of students retained in 2004 is between 2.8% and 7.2%. The closest answer choice is D.

A University Wants to Increase Its Retention Rate of 4