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 class’s 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

Answer 1

To determine the z-statistic, we need to use the formula:

z = (x - μ) / (σ / sqrt(n))

Where:

x = sample mean (529)

μ = population mean (514)

σ = population standard deviation (117)

n = sample size (50)

Substituting the values, we get:

z = (529 - 514) / (117 / sqrt(50))

z = 1.26

Therefore, the correct z-statistic for this situation is 1.26 (option C). This indicates that Colleen's class's average math SAT score is 1.26 standard deviations above the population mean.