Question

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?
0.02
0.91
1.26
5.67

Explanation:

Step1: Identify the formula for z - statistic

The formula for the z - statistic in a sampling distribution of the 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 given values

We are given that $\mu = 514$, $\sigma=117$, $\bar{x} = 529$, and $n = 50$.

Step3: Substitute the values into the formula

$z=\frac{529 - 514}{\frac{117}{\sqrt{50}}}=\frac{15}{\frac{117}{\sqrt{50}}}$. First, calculate $\frac{117}{\sqrt{50}}\approx\frac{117}{7.071}\approx16.55$. Then, $z=\frac{15}{16.55}\approx0.91$.

Answer:

0.91 (corresponding to the second option in the multiple - choice list)