Quarter 4 Module 6: Computing Test Statistic on Population

Statistics and Probability

Quarter 4 – Module 6:

Computing Test Statistic on

Population Mean

Development Team of the Module

Writer: Nelda L. Oabel

Editors: Jerome A. Chavez, Gilberto M. Delfina, Garry S. Villaverde, and Pelagia L.

Manalang

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Statistics and

Probability Module 6:

Computing of Test Statistic on

Population Mean

ii

Introductory Message

For the facilitator:

Welcome to the Statistics and Probability for Senior High School Alternative

Delivery Mode (ADM) Module on Computing Test Statistic on Population

Mean!

This module was collaboratively designed, developed, and reviewed by

educators both from public and private institutions to assist you, the

teacher or the facilitator, in helping the learners meet the standards set by

the K to 12 Curriculum while overcoming their personal, social, and

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body of the module:

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encourage and assist the learners as they do the tasks included in the

module.

Notes to the Teacher

This contains helpful tips or strategies

that will help you in guiding the

learners.

iii

For the learner:

Welcome to the Statistics and Probability for Senior High School Alternative

Delivery Mode (ADM) Module on Computing Test Statistic on Population

Mean!

The hand is one of the most symbolical parts of the human body. It is often

used to depict skill, action, and purpose. Through our hands, we may learn,

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What I Need to

Know

This will give you an idea of the skills or

competencies you are expected to learn

in the module.

What I Know

This part includes an activity that aims

to check what you already know about

the lesson to take. If you get all the

answers correct (100%), you may decide

to skip this module.

What’s In

This is a brief drill or review to help you

link the current lesson with the previous

one.

What’s New

In this portion, the new lesson will be

introduced to you in various ways such

as a story, a song, a poem, a problem

opener, an activity, or a situation.

What Is It

This section provides a brief discussion

of the lesson. This aims to help you

discover and understand new concepts

and skills.

What’s More

This comprises activities for independent

practice to solidify your understanding

iv

and skills of the topic. You may check

the answers to the exercises using the

Answer Key at the end of the module.

What I Have Learned

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sentences/paragraphs to be filled in to

process what you learned from the

lesson.

What I Can Do

This section provides an activity which

will help you transfer your new

knowledge or skill into real life

situations or concerns.

Assessment

This is a task which aims to evaluate

your level of mastery in achieving the

learning competency.

Additional

Activities

In this portion, another activity will be

given to you to enrich your knowledge or

skill of the lesson learned. This also

aims for retention of learned concepts.

Answer Key This contains answers to all activities in

the module.

At the end of this module, you will also find:

The following are some reminders in using this module:

1. Use the module with care. Do not put unnecessary mark/s on any part of

the module. Use a separate sheet of paper in answering the exercises.

2. Don’t forget to answer What I Know before moving on to the other

activities included in the module.

3. Read the instruction carefully before doing each task.

4. Observe honesty and integrity in doing the tasks and checking your

answers.

5. Finish the task at hand before proceeding to the next.

6. Return this module to your teacher/facilitator once you are through with

it.

If you encounter any difficulty in answering the tasks in this module, do not

hesitate to consult your teacher or facilitator. Always bear in mind that you

are not alone.

We hope that through this material, you will experience meaningful learning

and gain deep understanding of the relevant competencies. You can do it!

References This is a list of all sources used in

developing this module.

1

What I Need to Know

In this module, you will learn how to compute the test statistic on a

population mean particularly the t-test and z-test. It is a skill that you need

to develop to be able to determine whether you reject the null hypothesis or

otherwise (to be discussed in the next module). Perform each activity

independently. If you find any difficulty in answering the exercises, you may

ask the assistance of your teacher or you may consult your peers.

After going through this module, you are expected to:

1. determine the appropriate test statistic to be used in the given

problem/situation; and

2. compute for the test statistic value (population mean).

What I Know

Directions: Choose the best answer to the given questions or statements.

Write the letter of your choice on a separate sheet of paper. 1. It refers to a value calculated from sample data which is needed in

deciding whether the null hypothesis is rejected or not.

A. test statistics C. null hypothesis

B. critical region D. alternative hypothesis 2. What test statistic will be used if the sample size is above 30?

A. t-test C. population mean

B. z-test D. standard deviation

3. What test statistic can be used when the population standard deviation

is known?


B. z-test D. standard deviation 4. What test statistic can be used when the population standard deviation

is unknown?

A. t – test C. population mean

B. z – test D. standard deviation

2

5. When finding the z-computed value, which formula should be used for

hypothesis testing?

A. 𝑧 = �̅�−𝜇

𝜎

√𝑛

B. 𝑧 = �̅�−𝜇

𝑠

√𝑛

C. 𝑧 = 𝜇− �̅�

𝑠

√𝑛

D. 𝑧 = 𝜇− �̅�

𝜎

√𝑛

6. When should you use the t-test?

I. When you are testing for a population mean

II. When the sample standard deviation is given

III. When the population standard deviation is given

IV. When you are testing a proportion/percentage of a

population

A. I and II B. II and III C. I and III D. II and IV

For nos. 7-8, refer to the problem below:

Given: 𝐻𝑜: μ = 8.6 𝐻𝑎: μ > 8.6 The study has a sample mean of 9.1 and a standard deviation of 2.1

conducted among 25 respondents. Use 𝛼 = 0. 05.

7. What test statistics should be used?


B. z-test D. standard deviation 8. What is the computed value?

A. -1. 190 B. – 0. 567 C. 0. 567 D. 1.190

9. How many samples are best when dealing with z-test?

A. cannot be determined C. smaller than 30

B. exactly 30 D. equal or larger than 30

For nos. 10 – 12, refer to the given problem below:

The Choco Toppings, Inc. is one of the manufacturers of chocolate

toppings which uses a machine to dispense liquid ingredients into bottles

that move along a filling line. The owner claims that the machine can

dispense at an average of 50 grams with a standard deviation of 0.7 grams.

A sample of 35 bottles was selected and it was found out that the average

amount dispensed in the sample is 49.3 grams. Test the claims of the owner

of the company at 5% level of significance.

10. Which of the following information is correct?

A. 𝛼 = 0.5 B. 𝜎 = 0.7 C. �̅� = 35 D. 𝜇 = 49.3

11. What test statistic will be used?



3

12. Find the computed value.

A. -5.916 B. -4.950 C. 4.950 D. 5.916

13. Which test statistic will be used if the sample size is 15?

A. t-test C. cannot be determined

B. z-test D. neither t-test nor z-test

14. Which statistical method can you use when you have a normal

distribution of data?

A. t–test only C. either t–test or z–test

B. z–test only D. neither t–test nor z–test

15. A tire manufacturer claims that its tires have a mean life of 40,000 km. A

random sample of 46 of these tires is tested and the sample mean is

38,000 km. Assume that the population’s standard deviation is 2,000 km

and the lives of the tires are approximately normally distributed.

Determine the computed value at 5% level of significance.

A. -6.782 B. -3.033 C. 3.033 D. 6.782

How do you find this pre-test? Did you encounter both familiar and

unfamiliar terms? Kindly compare your answer in the Answer Key on the

last part of this module

If you obtain 100% or a perfect score, skip the module and

immediately move to the next module. But if you missed a point, please

proceed with the module as it will enrich your knowledge in computing the

test statistic.

4

Lesson

1 Computing Test Statistic on Population Mean

One of the steps in hypothesis testing is the computation of test

statistic. Remember that it is the value calculated from a sample data

which is needed whether you reject the null hypothesis or not.

Do you still remember when to use t-test? How about z-test? Answer

the activity that follows for a short review on t-test and z-test.

What’s In

Is It T or Z?

Directions: Identify the appropriate test statistic to be used based on the

given information. Write T if it is t-test and Z if it is z-test. 1. The sample mean is 345 and the sample size is 46. The population is

normally distributed with a standard deviation of 11. Test the hypothesis

at 0.05 level of significance. Consider the hypotheses below:

𝐻𝑜: 𝜇 = 342 𝐻𝑎: 𝜇 ≠ 342

2. Test at 𝛼 = 0.05 the null hypothesis 𝐻𝑜: 𝜇 = 2. 19 against the alternative

hypothesis 𝐻𝑎: 𝜇 < 2. 19 with 𝑛 = 18, �̅� = 1.36, and 𝑠 = 0.14. Assume that

the population is approximately normal.

3. The sample size is less than 18 and the standard deviation is 3. 67.

4. �̅� = 125.3 𝑠 = 5 𝜇 = 124 𝑛 = 24 𝛼 = 0.05

5. �̅� = 25.4 𝜇 = 22.6 𝜎 = 15 𝑛 = 118 𝛼 = 0.01

Were you able to answer all the questions correctly? If yes, the next

activity will be easy for you. If not, go back your notes about the test

concerning means.

5

What’s New

t-Test vs z-Test

Directions: Complete the diagram below.

YES NO

YES NO

I think you are very much ready for this topic. Read, analyze, and

study the given examples carefully.

What Is It

There are two specific test statistics used for hypothesis testing

concerning means: z-test and t-test.

If the sample size is large, where 𝑛 ≥ 30 and the population standard

deviation (𝜎) is known, use z-test.

In finding the z-value, use the formula below:

𝑧 = �̅� − 𝜇

𝜎

√𝑛

where: �̅� = sample mean 𝜇 = population mean

𝑛 = sample size 𝜎 = population standard deviation

Do you know the standard deviation (σ)?

1.Use:

__________

Is the sample

size above

30?

2. Use:

__________

3. Use:

__________

6

On the other hand, t- test is used when 𝑛 < 30, the population is

normal or nearly normal, and sample standard deviation (𝑠) is unknown.

The formula for the t- value is:

𝑡 = �̅� − 𝜇

𝑠

√𝑛

where: �̅� = sample mean 𝜇 = population mean

𝑛 = sample 𝑠 = sample standard deviation The degrees of freedom is 𝑛 − 1 or 𝑑𝑓 = 𝑛 − 1.

Study the following examples.

Example 1: Compute the z-value given the following information. Use one-

tailed test and 0. 05 level of significance.

�̅� = 70 𝜇 = 71.5 𝜎 = 8 𝑛 = 100 Solution: Since σ is known and n ≥ 30, we will use z-test. Thus, we have:

Example 2: In the first semester of the school year, a random sample of 200

students got a mean score of 81.72 with a population standard deviation of

15 in Statistics and Probability test. The population mean is 79.83. Use 0.05

level of significance.

Solution: To answer the problem, let us first identify the given. We have:

�̅� = 81.72 𝜇 = 79.83 𝜎 = 15 𝑛 = 200

Since σ is known and n ≥ 30, we will use z-test.

Use the formula for z-test.

Substitute the given value to the formula.

Simplify.

Therefore, the computed z-value is 1.875.

𝑧 = �̅� − 𝜇

𝜎

√𝑛

𝑧 = 71. 5 − 70

8

√100

𝑧 = 1.5

8

10

𝑧 = 1.5

0.8

𝐳 = 𝟏. 𝟖𝟕𝟓

7

In Central Limit Theorem, the sample standard deviation (𝑠) may be

used as an estimate of the population standard deviation (𝜎) when the value

of 𝜎 is unknown. Consider the given examples below: Example 3: In the past, the average length of an outgoing call from a

business office has been 140 seconds. A manager wishes to check whether

that average has decrease after the introduction of policy changes. A sample

of 150 telephone calls produced a mean of 135 second, with a standard

deviation of 30 seconds. Perform the relevant test at 1% level of significance.

Solution: Let us first identify the given. We have:

�̅� = 135 𝜇 = 140 𝑠 = 30 𝑛 = 150

Since n ≥ 30, we will use z-test by replacing 𝝈 with its estimate s.


Substitute the given value to the

formula.

Simplify.

𝑧 = �̅� − 𝜇

𝜎

√𝑛

𝑧 = 81.72 − 79. 83

15

√200

𝑧 = 1. 89

1514. 14

𝑧 = 1. 89

1.06

𝐳 = 𝟏. 𝟕𝟖𝟑

Therefore, the computed z-value is

1.783.



formula.

Simplify.

𝑧 = �̅� − 𝜇

𝜎

√𝑛

𝑧 = 135 − 140

30

√150

𝑧 = −5

3012.25

𝑧 = −5

2.45

𝐳 = − 𝟐. 𝟎𝟒𝟏

Therefore, the computed z – value

is -2.041.

8

Example 4: Compute the t-value given the following information:

�̅� = 129.5 𝜇 = 127

𝑠 = 5 𝑛 = 12

Solution: Since σ is unknown and n < 30, we will use t-test. Thus, we have:

Example 5: The government claims that the monthly expenses of a Filipino

family with four members is P10,000. A sample of 26 family’s expenses has

a mean of P10,900 and a standard deviation of P1,250. Is there enough

evidence to reject the government’s claim at 𝛼 = 0. 01?

Solution: Let us first identify the given, so we have:

�̅� = P10,900 𝜇 = P10,000 𝑠 = P1,250 𝑛 = 26

Use the formula for t-test.


formula.

Simplify.

𝑡 = �̅� − 𝜇

𝑠

√𝑛

𝑡 = 10 900 − 10 000

1 250

√26

𝑡 = 900

1 2505.10

𝑡 = 900

245. 10

𝐭 = 𝟑. 𝟔𝟕𝟏

Therefore, the computed t-value is

3.671.

Use the formula for t-test.


formula.

Simplify.

𝑡 = �̅� − 𝜇

𝑠

√𝑛

𝑡 = 129. 5 − 127

5

√12

𝑡 = 2. 5

53.46

𝑡 = 2.5

1.44

𝐭 = 𝟏. 𝟕𝟑𝟔

Therefore, the computed t – value

is 1. 736.

9

Now, it’s your turn to answer the following exercises.

What’s More

Activity 1: Find My z-Value!

Directions: Find the computed z-value of the following. Write your answer

to the nearest thousandths. Show your solutions.

1. �̅� = 21. 75

𝜇 = 20. 83

𝜎 = 2.75

𝑛 = 38

2. �̅� = 11. 23

𝜇 = 12. 01

𝜎 = 3.0

𝑛 = 44

3. �̅� = 891.75

𝜇 = 890. 25

𝜎 = 11.75

𝑛 = 90

4. �̅� = 45 000

𝜇 = 46 100

𝜎 = 1 795

𝑛 = 50

5. �̅� = 1.72

𝜇 = 1.83

𝜎 = 1.05

𝑛 = 36

10

Activity 2: Find My t-Value!

Directions: Compute the t-value of the following. Write your answer to the

nearest thousandths. Show your solutions.

1. �̅� = 16.4

𝜇 = 15.86

𝑠 = 1.25

𝑛 = 21

2. �̅� = 246

𝜇 = 245. 85

𝑠 = 3.25

𝑛 = 29

3. �̅� = 9.5

𝜇 = 8.25

𝑠 = 1.45

𝑛 = 16

4. �̅� = 1.83

𝜇 = 1. 27

𝑠 = 2.15

𝑛 = 10

5. �̅� = 30. 18

𝜇 = 31. 23

𝑠 = 3.15

𝑛 = 23

Activity 3: Compute Me!

Directions: Solve the following. Write your answer to the nearest

thousandths.

11

1. �̅� = 7.7

𝜇 = 8.1

𝜎 = 5

𝑛 = 135

2. �̅� = 19.8

𝑠 = 4

𝜇 = 18.3

𝑛 = 11

3. �̅� = 12.5

𝑠 = 3

𝜇 = 10.75

𝑛 = 18

4. �̅� = 125.3

𝑠 = 5

𝜇 = 124

𝑛 = 24

5. �̅� = 25.4

𝜇 = 22.6

𝜎 = 15

𝑛 = 118

6. �̅� = 18.1

𝑠 = 3

𝜇 = 19.2

𝑛 = 15

7. �̅� = 98.7

𝜇 = 4.6

𝜎 = 99.1

𝑛 = 105

8. �̅� = 129.1

𝑠 = 7

𝜇 = 128.3

𝑛 = 23

9. �̅� = 17.2

𝜇 = 3.1

𝜎 = 16.9

𝑛 = 100

Activity 4: Find My Value!

Directions: Determine the test statistic used. Then, find the value of the

following based on the given information.

12

1. 𝐻𝑜: 𝜇 = 85 𝐻𝑎: 𝜇 ≠ 85

The sample mean is 83, the sample size is 39, and the standard

deviation is 5. Use 𝛼 = 0.05.

2. 𝐻𝑜: 𝜇 = 7. 5 𝐻𝑎: 𝜇 > 7. 5

The sample mean is 8.3 and the sample size is 52. The population

follows a normal distribution with standard deviation 3.17. Use 𝛼 =

0.01.

3. 𝐻𝑜: 𝜇 = 15 𝐻𝑎: 𝜇 < 15

The sample mean is 10, the sample standard deviation is 6.1, and the

sample size is 9. Use 𝛼 = 0.05.

4. 𝐻𝑜: 𝜇 = 116.12 𝐻𝑎: 𝜇 > 116.12

The population follows a normal distribution with standard deviation

of 7.18, sample mean of 118.7, and sample size of 21. Use 𝛼 = 0.10.

5. 𝐻𝑜: 𝜇 = 215 𝐻𝑎: 𝜇 ≠ 215

The population is approximately normal. The sample mean is 219.3,

the sample standard deviation is 13.12, and the sample size is 22.

Use 𝛼 = 0.05.

6. 𝐻𝑜: 𝜇 = 15 𝐻𝑎: 𝜇 ≠ 15

The population is approximately normal. The sample mean is 15.3,

the sample standard deviation is 2.5, and the sample size is 12. Use 𝛼

= 0.05.

7. 𝐻𝑜: 𝜇 = 65 𝐻𝑎: 𝜇 > 65

The sample mean is 63, the sample size is 43, and the standard

deviation is 4. Use 𝛼 = 0.05.

13

8. 𝐻𝑜: 𝜇 = 25 𝐻𝑎: 𝜇 < 25

The sample mean is 23.75, the sample standard deviation is 4.5, and

the sample size is 12. Use 𝛼 = 0.05.

9. 𝐻𝑜: 𝜇 = 106.22 𝐻𝑎: 𝜇 > 106.22

The population follows a normal distribution with standard deviation

of 4.08, sample mean of 108.5 and sample size of 17. Use 𝛼 = 0.10.

10. 𝐻𝑜: 𝜇 = 25. 5 𝐻𝑎: 𝜇 > 25. 5

The sample mean is 23.8 and the sample size is 42. The population

follows a normal distribution with standard deviation 2.27. Use

𝛼 = 0.01.

What I Have Learned

Directions: What new realizations did you have about the computation of test

statistic? To answer the question, complete the sentences below.

1. The __________ is used if the sample size is large, 𝑛 ≥ ___, and the

population standard deviation (𝜎) is __________.

2. The formula of the z-test is __________.

3. The __________ is used when 𝑛 < 30, the population is normal or nearly

normal, and sample standard deviation (𝑠) is __________.

4. The formula of the t-test is __________.

5. The formula for degree of freedom is __________.

14

What I Can Do

The Corona!

Directions: Determine the test statistic to be used, then find its computed

vale.

The Coronavirus Disease (COVID-19) is an infectious disease caused

by a new strain of coronavirus. The World Health Organization (WHO) claims

that the incubation period of the virus in the infected person has a mean of

5.1 days. The doctors in the Philippines conducted a research and they

found out that incubation period of the virus in human body is 6.03 days

with a standard deviation of 3.32. The samples were 46 COVID patients. Is

there enough evidence to conclude that the incubation period of the virus is

5.1 days as stated, at 𝛼 = 0. 01?

15

Assessment

Directions: Choose the best answer to the given questions or statements.

Write the letter of your choice on a separate sheet of paper. 1. What test statistic will be used if the sample size is below 30?



2. In using t-test for a population mean, we assume that the sample is

selected randomly. The given statement is:

A. always true C. sometimes true

B. always false D. sometimes false 3. If the population standard deviation is unknown, what test statistic is to

be used?



4. In finding the t-computed value, which formula should be used?

A. 𝑡 = 𝜇− �̅�

𝜎

√𝑛

B. 𝑡 = 𝜇− �̅�

𝑠

√𝑛

C. 𝑡 = �̅�−𝜇

𝑠

√𝑛

D. 𝑡 = �̅�−𝜇

𝜎

√𝑛

5. When should you use the z-test?

I. When you are testing for a population mean

II. When the population standard deviation is given

III. When the sample standard deviation ONLY is given

IV. When you are testing with small sample sizes, n < 30.

A. I and II C. II and IV

B. II and III D. I and III For nos. 6-8, refer to the problem below:

Milky Milk is sold in packets with an advertised mean weight of

0.5kgs. The standard deviation is known to be 0.11 kilograms. A consumer

group wishes to check the accuracy of the advertised mean and takes a

sample of 36 packets finding an average weight of 0.47kgs. 6. What test statistic should be used?



16

7. What is the sample size?

A. 0. 15 B. 0. 48 C. 0. 5 D. 36

8. What is the computed value?

A. – 1. 636 B. -1.488 C. 0. 833 D. 5. 551 For nos. 9-10, refer to the problem below:

Given: 𝐻𝑜: μ = 7.25 𝐻𝑎: μ < 7.25

The study has a sample mean of 8.1 and a standard deviation of 1.18

conducted among 15 respondents. Use 𝛼 = 0.01.

9. What test statistic should be used?



10. What is the computed value?

A. – 2.790 B. -2.368 C. 2.368 D. 2.790

11. How many samples are best when dealing with t-test?

A. cannot be determined C. smaller than 30

B. exactly 30 D. equal or larger than 30

12. Which test statistic will be used if the sample is 37?



13. Which statistical method can you use when you have a normal

distribution of data?

A. t-test only C. either t-test or z-test

B. z-test only D. neither t-test nor z-test

For nos. 14-15, refer to the problem below:

A tire manufacturer claims that its tires have a mean life of 40,000

kms. A random sample of 46 of these tires is tested and the sample mean is

38,000 kms. Assume that the populations standard deviation is 2,000 kms

and the lives of tires are approximately normally distributed. 14. What test statistic should be used?



15. What is the computed value at 5% level of significance?

A. 6.782 B. 3.033 C. -6.782 D. -3.033

17

Additional Activities

Directions: Answer the following:

1. Assume that the cholesterol levels in a certain population have mean µ =

150 and standard deviation σ = 12. The cholesterol levels for a random

sample of n = 40 individuals are measured and the sample mean x is

determined. What is the computed value at 𝛼 = 0. 01 if �̅� = 147?

2. The maximum heart rate of a person at the age of 20 is 200 beats per

minute. Conduct a survey with your neighbors whose age is between 15-

20. Collect a data of 10 samples, then compute its value for 𝛼 = 0. 01?

18

Answer Key

What's In

(Is It T or Z?) 1.Z

2.T

3.T

4.T

5.Z

What I Know 1.A 9. D

2.B 10. B 3.B 11. B

4.A 12. A 5.A 13. A

6.A 14. C 7.A 15. A

8.D

What's New

(t-Test vs z-Test) 1.z-test

2.z-test

3.t-test

What's More

Activity 1: Find My

z-Value!

1.2.063

2.-1.725

3.1.211

4.-4.333

5.-0.629

What's More

Activity 2: Find My

t-Value!

1.1.980

2.0.249

3.3.448

4.0.824

5.-1.599

What's More

Activity 3: Compute

Me

1. -0.930

2.1.244

3.2.475

4.1.275

5.2.028

6.-1. 420

7.-0.891

8.0.548

9.0.968

What's More

Activity 4: Find My

Value!

1.z-test; -2.498

2.z-test; 1.820

3.t-test; -2.459

4.t-test; 1.647

5.t-test; 1.537

6.t – test; 0.416

7.z – test; -3.279

8.t – test; -0.962

9.t – test; 2.304

10.z – test; -4.853

What I Can Do

The Corona

z-test; 1.900

19

Assessment

1.A 9. A

2.A 10. D 3.A 11. C

4.C 12. B 5.A 13. C

6.B 14. B

7.D 15. C 8.A

Additional

Activities 1. z = -1.581

2.Answers may vary.

What I Have

Learned

1.z-test; 30; known

2.𝑧= 𝑥−𝜇

𝜎

√𝑛

3.t-test; unknown

4.𝑡= 𝑥−𝜇

𝑠

√𝑛

5.df = n-1

20

References

Textbooks

Albacea, Zita VJ., Mark John V. Ayaay, Isidoro P. David, and Imelda E. De Mesa. Teaching Guide for Senior High School: Statistics and Probability. Quezon City:

Commision on Higher Education, 2016.

Caraan, Avelino Jr S. Introduction to Statistics & Probability: Modular Approach.

Mandaluyong City: Jose Rizal University Press, 2011.

De Guzman, Danilo. Statistics and Probability. Quezon City: C & E Publishing Inc., 2017.

Punzalan, Joyce Raymond B. Senior High School Statistics and Probability. Malaysia: Oxford Publishing, 2018.

Sirug, Winston S. Statistics and Probability for Senior High School CORE Subject A Comprehensive Approach K to 12 Curriculum Compliant. Manila: Mindshapers Co., Inc., 2017.

Online Resources

Lauer, Stephen A., Kyra H. Grantz, Qifang Bi, Forrest K. Jones, Qulu Zheng,

Hannah R. Meredith, Andrew S. Azman, Nicolas G. Reich, and Justin Lessler.

“The Incubation Period of Coronavirus. Disease 2019 (COVID-19) From

Publicly Reported Confirmed Cases: Estimation and Application,” Annals of

Internal Medicine 172, no. 9 (2020); 577-582. Accessed May 21, 2020

https://www.acpjournals.org/doi/10.7326/M20-0504

21

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Telefax: (632) 8634-1072; 8634-1054; 8631-4985

Email Address: [email protected] * [email protected]

Documents

Quarter 4 Module 6: Computing Test Statistic on Population