d) A politician urging tighter restrictions on drivers’ licenses issued to teens says, "In one of every five auto accidents, a teenager is behind the
Does the confidence interval contradict this statement?
A. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is inside the interval.
B. The confidence interval does not contradict the assertion of the politician. The figure quoted by the politician is outside the interval.
C. The confidence interval does not contradict the assertion of the politician. The figure quoted by the politician is inside the interval.
D. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is outside the interval.

Question

UpStudy AI · Accepted Answer

Let the proportion of accidents in which a teenager is involved be denoted by $$ p $$. The politician’s statement that “one of every five auto accidents” involves a teen implies

$$
p = 0.20.
$$

A confidence interval for $$ p $$ is typically constructed from sample data. In this case, if the confidence interval includes $$ 0.20 $$, then the observed data are consistent with the politician’s claim. That is, even if the point estimate from the sample differs slightly from $$ 0.20 $$, the interval suggests that a teen involvement rate of $$ 20\% $$ is plausible given the uncertainty.

Since the answer choice stating that “the figure quoted by the politician is inside the interval” and that it “does not contradict the assertion” is:

$$
\textbf{C. The confidence interval does not contradict the assertion of the politician. The figure quoted by the politician is inside the interval.}
$$

Thus, there is no contradiction if $$ 0.20 $$ lies inside the confidence interval.
The confidence interval does not contradict the politician's statement because the figure of 20% is inside the interval.

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