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?

Question

Julia

Mathematics

2 September, 09:56

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?

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Moises Berger · Answer 1

The z-score can be calculated by the difference of population and sample mean divided by standard error. Standard error can be calculated as the standard deviation divided by square root of sample size. From the given, the standard error: SE = 12/sqrt (20) = 2.68 Z = (208 - 195) / 2.68 = 4.85