Question

Which of the following are true? Select one or more:

(a) The t-distribution is dependent on the sample size.
(b) The t-distribution does not depend on the sample size.
(c) The t-distribution has more values at the extremes than a standard normal distribution.
(d) The t-distribution has fewer values at the extremes than a standard normal distribution.
(e) The t-distribution is bell-shaped and centered at its degrees of freedom.
(f) The t-distribution is bell-shaped and centered at 0.
(g) With larger samples, the t-distribution is closer to a normal distribution.
(h) With smaller samples, the t-distribution is closer to a normal distribution.

Answer 1

As given below.

Step-by-step explanation:

1. The t-distribution is based and dependent on the sample size.

2. The t-distribution is more valued at the extremes thus has a standard normal distribution.

3. The t-distribution is bell-shaped and is centered at 0.

4. The t-distribution is a kind of bell-shaped and is centered at its degrees of freedom.

5. With larger samples, the t-distribution is close to the normal distribution.

• Being symmetric in shape and a bell-shaped distribution of the normal distribution this is more prone to produce the values that are found its mean.

• Its an estimation of the unknown parameters and uncertainty of data. In case the deviation of the errors was known, the normal distribution would be used instead of the t-distribution or student's distribution.