Question

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

Explanation:

• Option A: The Student \(t\) - distribution is bell - shaped like the standard normal distribution (\(z\) - distribution).
• Option B: The Student \(t\) - distribution has a mean of \(t = 0\), but its standard deviation \(s=\sqrt{\frac{

u}{
u - 2}}\) (\(
u\) is the degrees of freedom and \(
u>2\)), not \(s = 1\). The standard normal distribution has a standard deviation of \(1\).

• Option C: The \(t\) - test is relatively robust against non - normality, especially for larger sample sizes.
• Option D: The shape of the Student \(t\) - distribution changes with the sample size (since the degrees of freedom \(

u=n - 1\) where \(n\) is the sample size).

Answer:

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