Question

The Insurance Institute for Highway Safety issued a press release titled "Teen Drivers Often Ignoring Bans on Using Cell Phones" (June 9, 2008). The following quote is from the press release.

Just 1–2 months prior to the ban's Dec. 1, 2006 start, 11 percent of teen drivers were observed using cell phones as they left school in the afternoon. About 5 months after the ban took effect, 12% of teen drivers were observed using cell phones.

Suppose that the two samples of teen drivers (before the ban, after the ban) can be regarded as representative of these populations of teen drivers. Suppose also that 200 teen drivers were observed before the ban (so

n₁ = 200

and

p̂₁ = 0.11)

and 150 teen drivers were observed after the ban.

(a) Construct a 95% confidence interval for the difference in the proportion using a cell phone while driving before the ban and the proportion after the ban. (Use p_before − p_after. Round your answers to three decimal places.)

Answer 1

Here, , n1 = 200 , n2 = 150
p1cap = 0.11 , p2cap = 0.12

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.11 * (1-0.11)/200 + 0.12*(1-0.12)/150)
SE = 0.0345

For 0.95 CI, z-value = 1.96
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.11 - 0.12 - 1.96*0.0345, 0.11 - 0.12 + 1.96*0.0345)
CI = (-0.078 , 0.058)