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 400 teen drivers were observed before the ban (so n, = 400 and p, = 0.11) and 175 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 phefore - Pater. Round your answers to three decimal places.) Interpret the interval. We are 95% confident that the true difference between the proportions of teenagers using a cell phones before and after the ban is between these two values. We are 95% confident that the true mean proportion of teenagers using a cell phones after the ban is between these two values. There is a 95% chance that the true difference between the proportions of teenagers using a cell phones before and after the ban is directly the middle of these two values. There is a 95% chance that the true mean proportion of teenagers using a cell phones before the ban is directly in the middle of these two values. O We are 95% confident that the true mean proportion of teenagers using a cell phones before the ban is between these two values. (b) Is zero included in the confidence interval of part (a)? What does this imply about the difference in the population proportions? Zero is included in the interval. This tells us that we have convincing evidence at the 0.05 confidence level of a difference between the proportion of teenagers using cell phones before and after the ban. O Zero is included in the interval. This tells us that we do not have convincing evidence at the 0.05 confidence level of a difference between the proportion of teenagers using cell phones before and after the ban. O Zero is not included in the interval. This tells us that we have convincing evidence at the 0.05 confidence level of a difference between the proportion of teenagers using cell phones before and after the ban. Zero is not included in the interval. This tells us that we do not have convincing evidence at the 0.05 confidence level of a difference between the proportion of teenagers using cell phones before and after the ban.

Answer 1

The statistical software output for this problem is:

Two sample proportion summary confidence interval:

p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions

95% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L. Limit	U. Limit
p1 - p2	44	400	21	175	-0.01	0.029123505	-0.067081022	0.047081022

Hence,

a) 95% confidence interval:

(-0.067, 0.047)

Interpretation: Option A is correct.

b) Option B is correct