a recent survey of 8,000 high school students found that the mean price of a prom dress was $195.00 with a…

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?\n0.24\n4.84\n7.51\n96.90

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?\n0.24\n4.84\n7.51\n96.90

Answer

Answer:

4.84

Explanation:

Step1: Identify the formula

$z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$

Step2: Define the variables

$\bar{x} = 208$ (sample mean), $\mu=195$ (population mean), $\sigma = 12$ (population standard - deviation), $n = 20$ (sample size)

Step3: Substitute the values

$z=\frac{208 - 195}{\frac{12}{\sqrt{20}}}$

Step4: Calculate the denominator

$\frac{12}{\sqrt{20}}\approx\frac{12}{4.472}\approx2.683$

Step5: Calculate the numerator

$208 - 195=13$

Step6: Calculate the z - statistic

$z=\frac{13}{2.683}\approx4.84$