Question

which of the following is not a characteristic of the t test?
choose the correct answer below.
a. the student t distribution is different for different sample sizes.
b. the student t distribution has the same general bell shape as the standard normal distribution.
c. the t test is robust against a departure from normality.
d. the student t distribution has a mean of t = 0 and a standard deviation of s = 1.

Explanation:

• Option A: The Student's t - distribution changes with sample size (degrees of freedom \(df=n - 1\)), so this is a characteristic.
• Option B: The Student's t - distribution is bell - shaped like the standard normal distribution, so this is a characteristic.
• Option C: The t - test is robust against some departures from normality (e.g., for moderately non - normal data with moderate sample sizes), so this is a characteristic.
• Option D: The Student's t - distribution has a mean of \(t = 0\), but the standard deviation is \(s=\sqrt{\frac{df}{df - 2}}\) for \(df>2\), not \(s = 1\) (the standard normal distribution has a standard deviation of 1).

Answer:

D. The Student t distribution has a mean of \(t = 0\) and a standard deviation of \(s = 1\).