Question

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

Explanation:

• Option A: 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 (\(z\) - distribution) has a mean of \(0\) and a standard deviation of \(1\).

• Option B: The t - test is relatively robust against moderate departures from normality.
• Option C: The shape of the Student t - distribution changes with the sample size (since the degrees of freedom, which are related to the sample size, affect its shape). For example, as the sample size (degrees of freedom) increases, the t - distribution approaches the standard normal distribution.
• Option D: The Student t - distribution is bell - shaped, similar to the standard normal distribution, but it has more spread (heavier tails) when the degrees of freedom are small.

Answer:

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