Last week, 108 cars received parking violations in the main university parking lot. Of these, 27 had unpaid parking tickets from a previous violation. Assuming that last week was a random sample of all parking violators, find the 95 percent confidence interval for the percentage of parking violators that have prior unpaid parking tickets.
A)18.1 to 31.9 percent.
B)16.8 to 33.2 percent.
C)15.3 to 34.7 percent.
D)19.5 to 30.5 percent.

Question

Quizplus · Accepted Answer

To find the confidence interval for the percentage of parking violators that have prior unpaid parking tickets, we will use the formula for confidence interval for a proportion:

p̂ ± z*√(p̂(1-p̂)/n)

where p̂ is the sample proportion (number of parking violators with prior unpaid parking tickets divided by the total sample size), z is the critical value for our desired level of confidence (95% corresponds to a z-value of approximately 1.96), and n is the sample size (number of parking violators).

Using the given information, we have:

- Sample proportion: p̂ = 27/108 = 0.25 
- Sample size: n = 108 
- Critical value: z = 1.96

Plugging these values into the formula, we get:

0.25 ± 1.96*√(0.25(1-0.25)/108)

Simplifying this expression gives us the 95% confidence interval:

0.168 to 0.332

Converting these decimal values to percentages, we get:

16.8% to 33.2%

Therefore, the best choice is B: 16.8 to 33.2 percent.

Last Week, 108 Cars Received Parking Violations in the Main