The t distribution is similar to the z distribution because _________________.
A)As the degrees of freedom go to infinity,the t distribution converges to the z distribution
B)Both have asymptotic tails-that is,their tails become closer and closer to the horizontal axis,but never touch it
C)Both A and B are correct
D)Neither A nor B is correct

Question

Quizplus · Accepted Answer

The t distribution is similar to the z distribution in two ways:
A) As the degrees of freedom increase, the t distribution approaches the normal (z) distribution. This means that they become more and more similar as the sample size (degrees of freedom) increases.
B) Both the t and z distributions have what are known as asymptotic tails. This means that the tails approach the horizontal axis, but never actually touch it. This is because the standard deviation can theoretically be any value greater than zero, so the tails of the distribution continue on indefinitely.

The T Distribution Is Similar to the Z Distribution Because