Question

What is the most common method to renew vehicle registration? In checking a random sample of 500 motor vehicle renewal registrations in one county, the finance department found that 200 were mailed, 160 were paid in person at the county finance department office, and the remainder was paid online at the county's website. Phone registration renewals were not available.

a. Estimate the population proportion to pay for vehicle registration renewals in person at the county finance department office. Use a 90% confidence level.

b. Estimate the population proportion of online renewals. Use a 95% confidence level

Answer 1

a) Sample proportion, p = 160/500 = 0.32

The formula for the confidence interval is:

z-critical value at 90% confidence level: +1.645 and -1.645

n = 500, p = 0.32

Inputting the values into the formula:

Lower bound: 0.32 - 1.645*√(0.32*0.68/500) = 0.32 - 0.0343 = 0.2857

Upper bound: 0.32 + 1.645*√(0.32*0.68/500) = 0.32 +  0.0343 = 0.3543

90% Confidence level: (0.2857, 0.3543)

b) Sample proportion, p =(500 - 200 - 160)/500 = 0.28

n = 500

z-critical value at 95% confidence level = 1.96

Inputting the values into the formula:

Lower bound: 0.28 - 1.96*√(0.28*0.72/500) = 0.28 - 0.0394 = 0.2406

Upper bound: 0.28 + 1.96*√(0.28*0.72/500) = 0.28 + 0.0394 = 0.3194

95% CI: (0.2406, 0.3194)