Question

Kristy randomly samples the out-of-state tuition and fees for 25 public universities and found a mean of $20,876 with a standard deviation of $2,494. Using the alternative hypothesis that µ < $21,706, Kristy found a z-test statistic of -1.66.

Given the data provided, what is the p-value of the z-test statistic? Answer choices are rounded to the thousandths place.

A) 0.045
B) 0.100
C) 0.095
D) 0.035

Answer 1

The p-value of the z-test statistic is 0.048, which is closest to option A) 0.045.

Step-by-step explanation:

To find the p-value of the z-test statistic, we need to determine the probability of obtaining a test statistic as extreme as -1.66 or less if the null hypothesis is true. Since our alternative hypothesis is that the mean is less than $21,706, the p-value represents the probability of obtaining a mean of $20,876 or lower.

Using a standard normal distribution table or a calculator, we can find that the area to the left of -1.66 on the standard normal curve is approximately 0.048, rounded to the thousandths place. This means that the p-value is 0.048, which is closest to option A) 0.045.