Chicago Connection, a local pizza company, delivers pizzas for free within the market area. The delivery drivers are paid $2.00 per delivery plus they get to keep any tips. To estimate the proportion of deliveries that result in a tip to the driver, a random sample of 64 deliveries was selected. Of these, 48 times a tip was received. Based on this information, and using a 95 percent confidence level, the margin of error for the estimate is approximately ±.1061.

Question

Quizplus · Accepted Answer

The margin of error (MOE) for a proportion is calculated using the formula $MOE = Z * \sqrt{\frac{p(1-p)}{n}}$, where $Z$ is the Z-score corresponding to the confidence level (for 95%, $Z = 1.96$), $p$ is the sample proportion, and $n$ is the sample size. Given $p = \frac{48}{64} = 0.75$ and $n = 64$, the calculation yields $MOE \approx 1.96 * \sqrt{\frac{0.75(0.25)}{64}} \approx 0.106$, which matches the provided margin of error.

Chicago Connection, a Local Pizza Company, Delivers Pizzas for Free