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

u}{
u - 2}}\) (\(
u>2\), where \(
u\) is the degrees of freedom), 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 Student t - distribution changes with different sample sizes (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 \(s = 1\)