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
The distribution has a mean of one is not correct. So D
Mean = 0
The correct answer is D) mean of 1.
To determine which of the given characteristics is not related to the Student's t distribution, we can go through each option and see if it fits with the properties of the 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 approaches the standard normal distribution (z-distribution) in shape and properties. So, this is not the characteristic that does not belong to the Student's t distribution.
B) Depends on degrees of freedom.
This statement is true. The t-distribution depends on the degrees of freedom which is a parameter that determines the shape of the distribution. Therefore, this is a characteristic of the Student's t distribution.
C) Symmetric distribution.
This statement is true. The Student's t distribution is symmetric around its mean. The mean is zero for t-distributions with large sample sizes and non-zero mean for small sample sizes. So, this is not the characteristic that does not belong to the Student's t distribution.
D) Mean of 1.
This statement is false. The mean of the Student's t distribution is always zero for t-distributions with large sample sizes. The mean is non-zero for t-distributions with small sample sizes, but it can vary and is not fixed at 1. Therefore, the characteristic "mean of 1" does not belong to the Student's t distribution.
So, the correct answer is D) mean of 1.