The mean annual tuition and fees for a sample of 12 private colleges was $36,800 with a standard deviation of $5000. 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 $33,700.
Compute the value of the test statistic and state the number of degrees of freedom.
A) 0.620; 12 degrees of freedom
B) 0.620; 11 degrees of freedom
C) 2.148; 12 degrees of freedom
D) 2.148; 11 degrees of freedom

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula $t = \frac{\bar{x} - \mu_0}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu_0$ is the hypothesized population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Here, $\bar{x} = 36800$, $\mu_0 = 33700$, $s = 5000$, and $n = 12$. Plugging these values into the formula gives $t = \frac{36800 - 33700}{(5000/\sqrt{12})} = 2.148$. The degrees of freedom for a t-test is $n - 1$, so with $n = 12$, the degrees of freedom is $11$.

The Mean Annual Tuition and Fees for a Sample of 12