Question

which of the following is not a property of the student t distribution?
choose the correct answer below.
a. the student t distribution has the same general symmetric bell shape as the standard normal distribution, but it reflects the greater variability that is expected with small samples.
b. the student t distribution has a mean of t = 0.
c. the standard deviation of the student t distribution is s = 1.
d. the student t distribution is different for different sample sizes.

Explanation:

• Option A: The \(t -\)distribution is symmetric (like the standard normal distribution) and has more variability (heavier - tails) for small samples. This is a property of the \(t -\)distribution.
• Option B: The mean of the \(t -\)distribution is \(t = 0\). This is a property of the \(t -\)distribution.
• Option C: The standard deviation of the \(t -\)distribution is \(s=\sqrt{\frac{

u}{
u - 2}}\) for \(
u>2\) (where \(
u\) is the degrees of freedom). It is not \(s = 1\) (the standard deviation of the standard normal distribution \(Z\) is \(\sigma=1\)). So this is not a property of the \(t -\)distribution.

• Option D: The \(t -\)distribution is parameterized by degrees of freedom \(

u=n - 1\) (where \(n\) is the sample size). Different sample sizes (\(n\)) lead to different degrees of freedom (\(
u\)), and thus different \(t -\)distributions. This is a property of the \(t -\)distribution.

Answer:

C. The standard deviation of the Student t distribution is \(s = 1\).