A simple random sample of 85 students is taken from a large university on the West Coast to estimate the proportion of students whose parents bought a car for them when they left for college.When interviewed,51 students in the sample responded that their parents bought them a car.What is a 95% confidence interval for p,the population proportion of students whose parents bought a car for them when they left for college?
A)(0.296,0.504)
B)(0.463,0.737)
C)(0.496,0.704)
D)(0.513,0.687)

Question

Quizplus · Accepted Answer

The sample proportion is 51/85 = 0.6. Using the formula for a confidence interval for a proportion, p ± Z*(sqrt(p(1-p)/n)), where Z is the Z-score for 95% confidence (approximately 1.96), the interval is calculated as 0.6 ± 1.96*(sqrt(0.6*0.4/85)), which results in the interval (0.496, 0.704).

A Simple Random Sample of 85 Students Is Taken from a Large