The document outlines a classroom activity focused on t-distribution, where students participate in various group tasks related to sampling distribution and vocabulary associated with statistics. It includes mechanics for group activities, analysis questions, examples of t-value calculations, quizzes, and an assignment on hypothesis definitions. By the end of the session, students are expected to illustrate t-distribution, participate actively, and solve for t-values and degrees of freedom.

1. STATISTIC AND PROBABILITY
T-DISTRIBUTION

2. ACTIVITY: MECHANICS
The teacher will group the class then ask the whole class
to recall the past lesson about sampling distribution then
they will write their answer (s) or ideas at the back of the
illustration board and raised it.
Each correct answer or nearest to the right answer will
earn 5 points that can be added to their performance.

3. WRITE YOUR ANSWERS AT THE BACK
OF THE ILLUSTRATION BOARD
Write 4 phrases that you
remember about our past lesson
about sampling distribution.

4. ACTIVITY: LOOK AT ME!
MECHANICS OF ACTIVITY:
1.I will divide your class into 3 groups.
2.I will post a puzzle in the board all you need to do is to
look for the hidden words
3.Students will be given 5 minutes to look for the hidden
words in the puzzle. Write it on the paper.
4.Each group will choose their representative that will
present their work in front.
5.Last, explain in your own idea the definition of those
words you found.

6. ANALYSIS QUESTIONS
1. What are the words you found?
a. Percentile
b. Distribution
c. T-table
d. T-value
e. Level of significance
f. Degree of freedom
2. What do you think is the connection of those words to our topic?
3. Have you encountered any difficulties in finding the hidden words?

7. OBJECTIVE:At the end of the session,
the students are able to:
a.Illustrate t-distribution.
b.Actively participate to given task;
c.Solve the degrees of freedom to get the t-
value of a certain data.

8. VOCABULARY WORDS
Percentile- This is a measure of position with data divided into 100 parts.
Degree of freedom- This refers to the maximum number of logically
independent values which vary in the data sample.
T-table-is a reference statistical table that contains critical values of the t
distribution, also known as the t-score or t- value.
Level of significance- the measurement of the statistical significance.
T-value-the ratio of the difference between the mean of the two sample
sets and the variation that exists within the sample sets.
Distribution- function that shows the possible values for a variable and
how often they occur.
T-distribution- student’s t-distribution

9. ILLUSTRATION OF T-DISTRIBUTION

11. FORMULA FOR DETERMIING
DEGREES OF FREEDOM
df=n-1

12. EXAMPLE 1
Identify the t-value whose number of
samples n=7 and has an area equal to
0.05. Under one-tailed test.

13. Solution:
Using the formula:
df=n-1
df= 7-1
df= 6
The t-value is equal to 1.9432

14. EXAMPLE 2
Let us have another example:
Given the df=10 and has an area of
0.02. Identify the t-value under two-
tailed test.

15. Answer: 2.7638

16. EXAMPLE 3
Identify the t-value whose
number of samples n=23 and
has an area (a) equal to 0.
0005.

17. Solution using the formula.
df=n-1
df=23-1
df=22
Therefore the degrees of freedom is
equivalent to 22.

18. The t-value is equal to 3.7921

19. Group Activity:
So here’s the procedure.
1. Using the same group.
2. I will be giving you 7 questions.
3. Assign a number for each member
(1,2,3,4,5,6,7).
4. Then, I will call a certain number to go in front
and answer.

20. Questions:
1. What is the value of the degrees of freedom when
the sample size is 14?
2. T-distribution is also called___________?
3. This refers to a measure of position with data divided
into.
4. Identify the t-value whose number of samples n=3
and has an area (a) equal to 0.10 on one tailed test.
5. Given the degrees of freedom= 5 and the area is
0.01 . What is the t-value under one-tailed test?

21. Answers:
1.Df=13
2.Students t-distribution
3.Percentile
4.1.885618
5.3.36493
6.Degree of freedom
7.Normal distribution

22. Quiz:Direction: Choose the letter of
the correct answer.
1. What is the other term for t-distribution?
a. Z-distribution
b. Probability distribution
c. Percentile distribution
d. Student’s t-distribution
2. This refers to the maximum number of logically independent values
which varies in the data sample.
a. Level of significance
b. Percentiles
c. Degree of freedom
d. Probability

23. 3. This is a measure of position with data divided into 100 parts.
a. Percentile
b. Degree of freedom
c. T-distribution
d. Level of significance
4. What will be the degree of freedom of the data whose sample size is
18?
a. 17 b. 18
c. 19 d. 20
5. Which of the following is NOT a characteristics of T-distribution?
a. The T-distribution has a smooth shape
b. The T-distribution is symmetric
c. The t-distribution has a mean of 1

24. Answers:
1. D
2. C
3. A
4. A
5. C

25. Assignment: Search for the definition of
the following.
1.Null Hypothesis
2.Alternative Hypothesis