STATISTICAL TECHNIQUES AND TOOLS
CONFIDENCE INTERVALS
|
Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
|
Which of the following statements is (are) true about the t-distribution with k degrees of freedom?I. The t-distribution is symmetric.II. The t-distribution with k degrees of freedom has a smaller variance than the t-distribution with k + 1 degrees of freedom.III. The t-distribution has a larger variance than the standard normal (z) distribution.
|
|
I only
|
|
|
II only
|
|
|
III only
|
|
|
I and II
|
|
|
I and III
|
Explanation:
Detailed explanation-1: -The t distribution has the following properties: The mean of the distribution is equal to 0 . The variance is equal to v / ( v-2 ), where v is the degrees of freedom (see last section) and v > 2. The variance is always greater than 1, although it is close to 1 when there are many degrees of freedom.
Detailed explanation-2: -As the DF decreases, the t-distribution has thicker tails. This property allows for the greater uncertainty associated with small sample sizes.
There is 1 question to complete.