Question

A random sample of 20 students at a large university has a mean GPA of 3.27. GPAs at the university are known to follow a normal distribution with standard deviation 0.51 . In carrying out a test of significance to determine whether there is evidence that the true mean GPA of students at the university differs from 2.93, the p-value is found to be 0.0028691 . The correct interpretation of this p-value is:

(A) If the true mean GPA of all students at the university was not equal to 2.93 , the probability of observing a sample mean larger than 3.27 would be 0.0028691 .
(B) If the true mean GPA of all students at the university was not equal to 2.93 , the probability of observing a sample mean at least as extreme as 3.27 would be 0.0014346 .

Answer 1

The p-value is the probability of observing a sample mean as extreme as or more extreme than what is observed. If the p-value is less than the significance level, we can reject the null hypothesis.

Step-by-step explanation:

The p-value is the probability of observing a sample mean as extreme as or more extreme than what is observed, assuming that the null hypothesis is true. In this case, the p-value is 0.0028691. Since this p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence that the true mean GPA of students at the university differs from 2.93.