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. The test statistic is
A)1.96
B)2.00
C)1.645
D)0.05

Question

Quizplus · Accepted Answer

To calculate the test statistic for a one-sample t-test, we use the formula:

t = (sample mean - hypothesized mean) / (standard error)

In this case, the sample mean is 25, the hypothesized mean is 24, and the standard error is the population standard deviation divided by the square root of the sample size:

SE = 2 / sqrt(16) = 0.5

Plugging in these values, we get:

t = (25 - 24) / 0.5 = 2

Therefore, the test statistic is 2, which corresponds to the B choice. Note that we use a t-distribution because we do not know the population standard deviation and are estimating it from the sample.

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