Which of the following is not a characteristic of Students' t distribution?

A) For large samples, the t and z distributions are nearly equivalent.
B) depends on degrees of freedom.
C) symmetric distribution
D) mean of 1

d

The correct answer is D) mean of 1.

To determine which of the options is not a characteristic of the Students' t distribution, we will examine each option and the corresponding characteristic of the t-distribution.

A) For large samples, the t and z distributions are nearly equivalent.
This statement is true. As the sample size increases, the t-distribution converges to the standard normal (z) distribution. Therefore, option A is a characteristic of the t-distribution.

B) Depends on degrees of freedom.
This statement is true. The t-distribution is dependent on the degrees of freedom (df), which determines the shape of the distribution. As the degree of freedom increases, the t-distribution becomes more similar to the standard normal distribution. Therefore, option B is a characteristic of the t-distribution.

C) Symmetric distribution.
This statement is also true. The t-distribution is symmetric around its mean of zero. Therefore, option C is a characteristic of the t-distribution.

D) Mean of 1.
This option is not a characteristic of the t-distribution. The mean of the t-distribution is always equal to zero and not equal to 1. Therefore, option D is not a characteristic of the t-distribution.

In conclusion, the correct answer is option D) Mean of 1, as it does not describe a characteristic of the Students' t distribution.