the college board states that the average math sat score is 514 with a standard deviation of 117. colleen…
the college board states that the average math sat score is 514 with a standard deviation of 117. colleen gathered data from 50 students in her graduating class and found the average score to be 529. she thinks that her classs math sat score is different from the average. which of the following shows the correct z - statistic for this situation?\n0.02\n0.91\n1.26\n5.67
Answer
Explanation:
Step1: Identify the formula
The formula for the z - statistic of a sample mean is $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size.
Step2: Identify the values
We are given that $\mu = 514$, $\bar{x}=529$, $\sigma = 117$, and $n = 50$.
Step3: Substitute the values into the formula
First, calculate $\frac{\sigma}{\sqrt{n}}=\frac{117}{\sqrt{50}}\approx\frac{117}{7.071}\approx16.55$. Then, $z=\frac{529 - 514}{16.55}=\frac{15}{16.55}\approx0.91$.
Answer:
0.91