Exhibit 9-6
A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal.
-Refer to Exhibit 9-6. The p-value is between
A).005 to .01
B).01 to .025
C).025 to .05
D).05 to .10

Question

Quizplus · Accepted Answer

To determine the p-value, we use a one-sample t-test with a null hypothesis that the population mean age is 24 and an alternative hypothesis that the population mean age is greater than 24. With a sample size of 16, degrees of freedom is 15.
The t-value is calculated as:
t = (sample mean - hypothesized population mean)/(standard error of the mean) = (25-24)/(2/sqrt(16)) = 4
Using a t-distribution table with 15 degrees of freedom, we find that the probability of getting a t-value of 4 or higher is between 0.025 and 0.05. This is the p-value. Therefore, the answer is C.

Exhibit 9-6 A Random Sample of 16 Students Selected from the Student