Exhibit 9-4
A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years.
-Refer to Exhibit 9-4. At a .05 level of significance, 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 less than 25

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula for a z-test: $ z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} $. Here, $\bar{x} = 25$, $\mu = 24$, $\sigma = 2$, and $n = 16$. The calculated z-value is 2. The critical z-value for a two-tailed test at the 0.05 significance level is approximately ±1.96. Since 2 is greater than 1.96, we reject the null hypothesis, indicating the mean age is significantly different from 24.

Exhibit 9-4 A Random Sample of 16 Students Selected from the Student