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. At 95% confidence, it can be concluded that the mean age is
A)not significantly different from 24
B)significantly different from 24
C)significantly less than 24
D)significantly more than 24

Question

Quizplus · Accepted Answer

We can conduct a one-sample t-test to test the null hypothesis that the population mean age is 24 against the alternative hypothesis that it is greater than 24. Using a t-distribution with degrees of freedom (df) = 15 (n-1), we find the critical t-value with 95% confidence to be t(15, 0.05) = 1.753.

The test statistic is calculated as follows:
t = (sample mean - hypothesized mean)/(standard error)
standard error = standard deviation/sqrt(sample size) = 2/sqrt(16) = 0.5

t = (25 - 24)/0.5 = 2

Since our calculated t-value of 2 is greater than the critical t-value of 1.753, we reject the null hypothesis and conclude that the mean age of all the students at the university is significantly more than 24, with 95% confidence. Therefore, the answer is D, significantly more than 24.

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