The mean annual tuition and fees for a sample of 9 private colleges was $30,100 with a standard deviation of $5500. 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 $33,000.
Compute the value of the test statistic and state the number of degrees of freedom.
A)-0.527; 9 degrees of freedom
B)-0.527; 8 degrees of freedom
C)-1.582; 9 degrees of freedom
D)-1.582; 8 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, $\bar{x} = 30100$, $\mu = 33000$, $s = 5500$, and $n = 9$. Plugging these values into the formula gives $t = \frac{30100 - 33000}{(5500/\sqrt{9})} = \frac{-2900}{1833.33} \approx -1.582$. The degrees of freedom (df) for a one-sample t-test is $n - 1$, which is $9 - 1 = 8$.

The Mean Annual Tuition and Fees for a Sample of 9