12 A recent survey of 8,000 high school students found that the mean price of a prom dress was \( \$ 195.00 \) with a standard deviation of \( \$ 12.00 \). Alyssa thinks that her school is more fashion conscious and spent more than \( \$ 195.00 \). She collected data from 20 people in her high school and found that the average price spent on a prom dress was \( \$ 208.00 \). Which of the following is the correct \( z \)-statistic for this situation? 0.24 4.84 7.51 96.90

To calculate the \( z \)-statistic, you can use the formula: \[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \] Where: - \( \bar{x} \) is the sample mean (\$208.00) - \( \mu \) is the population mean (\$195.00) - \( \sigma \) is the population standard deviation (\$12.00) - \( n \) is the sample size (20) Now plug in your values: 1. Calculate the standard error (SE): \[ SE = \frac{12}{\sqrt{20}} \approx 2.68 \] 2. Now plug in the values to find the \( z \)-statistic: \[ z = \frac{208 - 195}{2.68} \approx 4.84 \] So, the correct \( z \)-statistic for this situation is **4.84**. If you ever find yourself in a similar scenario, remember that \( z \)-scores can help you understand how far away your sample mean is from the population mean, and they can elevate the drama in your statistical narrative! Always keep an eye on sample size as it greatly affects your standard error and overall results. Also, munch on this — when sampling, it's critical to ensure your sample is random and representative. Otherwise, your findings may lead you astray, like a runway model with clashing outfits on the catwalk!