An article in the San Jose Mercury News stated that students in the California state university system take 5 years, on average, to finish their undergraduate degrees. $A$ freshman student pelieves that the mean time is less and conducts a survey of 50 students. The student obtains a sample mean of 4.1 with a sample standard deviation of 0.7. Is there sufficient evidence to support the student's claim at an $\vartheta=0.01$ significance level? Determine the test statistic. Round to four decimal places.

Step 1 ：The student is conducting a one-tailed t-test to determine if the mean time to finish undergraduate degrees is less than 5 years. The null hypothesis is that the mean time is 5 years, and the alternative hypothesis is that the mean time is less than 5 years.

Step 2 ：The test statistic for a t-test is calculated as: \[ t = \frac{\bar{x} - \mu}{s/\sqrt{n}} \] where \(\bar{x}\) is the sample mean, \(\mu\) is the population mean, \(s\) is the sample standard deviation, and \(n\) is the sample size.

Step 3 ：In this case, \(\bar{x} = 4.1\), \(\mu = 5\), \(s = 0.7\), and \(n = 50\).

Step 4 ：Substituting these values into the formula, we get: \[ t = \frac{4.1 - 5}{0.7/\sqrt{50}} \]

Step 5 ：Solving this equation gives us the test statistic, which is approximately -9.0914. This value is negative because the sample mean is less than the population mean, which is consistent with the student's claim that the mean time to finish undergraduate degrees is less than 5 years.

Step 6 ：Final Answer: The test statistic is approximately \(\boxed{-9.0914}\).