Student’s t-distribution - Theory

Question 1

What is Student’s t distribution?

Answer 1

Basically many many bell-shaped curves that look similar to the bell-shaped curve of the SND but have lower peaks and higher tails than the SND curve

Question 2

What is the difference between all of Student’s t-distribution curves and the SND curve?

Answer 2

Student’s t-distribution curves have:

1) Lower peaks than SND curve
2) Higher tails than SND curve

Question 3

When is Student’s t-distribution used?

Answer 3

We can use the Student’s t-distribution instead of the SND when popupulation s.d. is unknown

Question 4

What is the formula for Student’s t-distribution?

Answer 4

t-score = (x - sample mean) / e.s.e.

What is e.s.e. = sample SD / SQRT (sample size)

Question 5

The t-distribution is very similar to the Standard Normal Distribution (SND) but, unlike the SND, there is only 1 t-distribution.

a. True
b. False

Answer 5

b. False

There are multiple t-distributions

Question 6

Complete the sentences:

The t-distribution is important when the population (……..) is unknown. In this case, we can not transform a sample mean to a (……….)

Instead, we use the sample (……….) to generate the (…………) and, subsequently a (………….)

Answer 6

1. s.d.
2. z-score
3. s.d.
4. e.s.e.
5. t-score

Question 7

Complete the sentences:

Student’s t-distribution is (………) the Standard Normal Distribution (SND). It is (………..), has (……….) and the area under the distibution is (………..).

All t-distributions with finite values of parameter v have a peak that is (…………) that of the SND and have tails that are (…………) those of the SND.

Answer 7

1. Similar to
2. Symmetric
3. A single mode
4. 1
5. Lower than
6. Higher than

Question 8

Complete the sentences:

As the parameter v gets smaller, the t-distribution gets (………) the Standard Normal Distribution.

As a consequence use of the t-distribution is particularly important for cases where we have a (…………) sample size.

Answer 8

1. Further from
2. Small