The mean annual tuition and fees for a sample of 8 private colleges was $33,700 with a standard deviation of $5,800. A dotplot shows that it is reasonable to assume that the population is Approximately normal. You wish to test whether the mean tuition and fees for private colleges is Different from $37,400.
Compute the value of the test statistic and state the number of degrees of freedom.
A) -1.804; 7 degrees of freedom
B) -1.804; 8 degrees of freedom
C) -0.638; 8 degrees of freedom
D) -0.638; 7 degrees of freedom

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula: $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean being tested against, $s$ is the sample standard deviation, and $n$ is the sample size. Here, $\bar{x} = 33700$, $\mu = 37400$, $s = 5800$, and $n = 8$. Plugging these values into the formula gives $t = \frac{33700 - 37400}{(5800/\sqrt{8})} = -1.804$. The degrees of freedom for a t-test is $n - 1$, which is $8 - 1 = 7$.

The Mean Annual Tuition and Fees for a Sample of 8