According to a "how to stop bullying" website, 15 percent of students report experiencing bullying one to three times within the most recent month.Assume the standard deviation is 4.5 percent of students.Joseph collects data from 175 students at a medium-sized school in Iowa and finds that only 12 percent reported this rate of bullying.What is his 95 percent confidence interval?
A) [7.5, 16.5]
B) [11.33, 12.67]
C) [11.94, 12.06]
D) [14.53, 15.67]

Question

Quizplus · Accepted Answer

The 95% confidence interval is calculated using the formula for the confidence interval of a proportion: CI = p ± Z*(σ/√n), where p is the sample proportion (12%), Z is the Z-score for a 95% confidence level (approximately 1.96), σ is the standard deviation (4.5%), and n is the sample size (175). Plugging these values into the formula gives a narrow interval around the sample proportion, which is closest to the range provided in option B.

According to a "How to Stop Bullying" Website, 15 Percent