Question

In a simple random sample of 352 students at a college, 92 reported that they have at least $1000 of credit card debt. What is the 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt?

1) (20.6, 31.6)
2) (22.3, 29.9)
3) (19.0, 33.2)
4) (20.1, 32.1)

Answer 1

The 99% confidence interval for the percent of all students at the college who have at least $1000 in credit card debt is (20.61%, 31.57%).

Step-by-step explanation:

To find the 99% confidence interval for the percent of all students at the college who have at least $1000 in credit card debt, we can use the formula for a confidence interval for a proportion:

Lower Bound = sample proportion - (Z * sqrt((sample proportion * (1 - sample proportion))/n))

Upper Bound = sample proportion + (Z * sqrt((sample proportion * (1 - sample proportion))/n))

where:

sample proportion = number of students with at least $1000 credit card debt / sample size

Z = z-value for the desired confidence level (2.576 for 99% confidence)

n = sample size

Plugging in the values from the given question: sample proportion = 92/352 = 0.26136

Lower Bound = 0.26136 - (2.576 * sqrt((0.26136 * (1 - 0.26136))/352)) = 0.20607

Upper Bound = 0.26136 + (2.576 * sqrt((0.26136 * (1 - 0.26136))/352)) = 0.3157

Therefore, the 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.61%, 31.57%). The correct option is 1) (20.6, 31.6).