Question

Driver’s License Rates. Fewer young people are driving. In 1995, 63.9% of people under 20 years old who were eligible had a driver’s license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample of 1200 people under 20 years old who were eligible to have a driver’s license in 1995 and again in 2016.

a. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver’s license in 1995?

b. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver’s license in 2016?

c. Is the margin of error the same in parts (a) and (b)? Why or why not?

Answer 1

a)

sample proportion, = 0.639
sample size, n = 1200
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.639 * (1 - 0.639)/1200) = 0.0139

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0139
ME = 0.0272

b)

sample proportion, = 0.417
sample size, n = 1200
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.417 * (1 - 0.417)/1200) = 0.0142

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0142
ME = 0.0278

c)

No, not same because proportion are different