To construct a confidence interval for the proportion of fatal accidents involving cell phones, use the sample proportion and a formula for the confidence interval.
To construct a confidence interval for the proportion of fatal accidents that involved the use of a cell phone, we can use a formula for calculating a confidence interval for a proportion.
The best point estimate for p, the proportion of fatal accidents involving cell phones, is the sample proportion, which is found by dividing the number of fatal accidents involving cell phones by the total number of non-fatal accidents.
In this case, the sample proportion is 162/500 = 0.324.
The formula for the confidence interval is: point estimate ± (z-score * standard error)
Since we want a 99% confidence interval, the z-score for a 99% confidence level is approximately 2.576. The standard error is the square root of [(point estimate * (1 - point estimate)) / sample size].
Plugging in the values, we get:
Standard error = sqrt((0.324 * (1 - 0.324)) / 500) ≈ 0.022
Confidence interval = 0.324 ± (2.576 * 0.022) = (0.272, 0.376)