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A survey of 300 non- fatal accidents showed that 108 involved uninsured drivers.

Construct a 99% confidence interval for the proportion of fatal accidents that involved uninsured
drivers. Round to the nearest thousandth.

User Sayth
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1 Answer

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The 99% confidence interval for the proportion of fatal accidents that involved uninsured drivers is approximately 0.316 to 0.404.

To construct a 99% confidence interval for the proportion of fatal accidents that involved uninsured drivers, we can use the formula:

CI = p ± z * sqrt((p * (1 - p)) / n)

Where p is the sample proportion, z is the z-value for the desired confidence level, and n is the sample size. In this case, the sample proportion is 108/300 = 0.36 and the sample size is 300.

Using a z-value of 2.576 (corresponding to a 99% confidence level), we can plug in the values:

CI = 0.36 ± 2.576 * sqrt((0.36 * (1 - 0.36)) / 300)

Simplifying the equation, the 99% confidence interval for the proportion of fatal accidents that involved uninsured drivers is approximately 0.316 to 0.404.

Therefore, we can be 99% confident that the true proportion falls within this interval.

User Alhuck
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