A random sample of 25 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. 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

We can use a one-sample t-test to determine if the average age of all students at the university is significantly more than 24. The null hypothesis would be that the true population mean is equal to 24, and the alternative hypothesis would be that it is greater than 24.

Using the information given, we can calculate the t-statistic as follows:

t = (sample mean - hypothesized mean) / (standard error)
t = (25 - 24) / (2 / sqrt(25))
t = 5

The degrees of freedom for this test would be 24, since we have a sample size of 25. Using a t-distribution table or calculator, we can find the p-value associated with a t-statistic of 5 and 24 degrees of freedom. The p-value turns out to be less than .05 but greater than .025. Therefore, the answer is C, between .025 to .05.

A Random Sample of 25 Students Selected from the Student