WHOLE BRAIN LEARNING SYSTEM
OUTCOME-BASED EDUCATION
GRADE
SENIOR HIGH SCHOOL
Statistics and Probability
LEARNING
MODULE
QUARTER
WEEK
11
4
1
1
MODULE IN
STATISTICS AND PROBABILITY
QUARTER 4
WEEK 1
Understanding
Hypothesis Testing
Development Team
Writers:
Editors/Reviewers:
Michael G. Calipjo
Jerick S. Paltong
Ma. Teresa R. Pascual
Vanessa A. Miguel
Gerson Jeremy C. Antonio
Myla Fei Martinez
Gregorio P. Agatep, Jr.
Illustrator:
Jeshimon C. Patoc
Layout Artist:
Vanessa A. Miguel
Management Team:
Vilma D. Eda
Arnel S. Bandiola
Lourdes B. Arucan
Juanito V. Labao
Marlyn S. Ventura
2
What I Need to Know
In this module, you will learn the fundamentals of hypothesis testing. It includes
definitions of terms and illustr
ations of those terms that will help you fully understand the concept of hypothesis
testing. This module also contains lessons on identifying the parameter to be tested in real-life
problems.
Most Essential Learning Competencies (MELCs)
The learner:
1. illustrates: (a) null hypothesis; (b) alternative hypothesis; (c) level of significance;
(d) rejection region; and (e) types of errors in hypothesis testing.
OBJECTIVES:
At the end of the module, the student must be able to:
1. illustrate (a) null hypothesis; (b) alternative hypothesis; (c) level of significance; (d)
rejection region; and (e) types of errors in hypothesis testing;
2. identify the parameter to be tested given a real-life problem; and
3. formulates the appropriate null and alternative hypotheses on a population mean.
3
What I Know
Directions: Read the questions carefully and choose the correct answer.
1. Which of the following best describes hypothesis testing?
A. It is a test of an educated guess to come up with a sound decision.
B. It is the examination of evidence to prove or disprove an argument.
C. It is a test of evidence to pronounce whether an argument is true or false.
D. It is a statistical method used in making decisions using experimental data.
2. Which of the following statements is incorrect?
A. A hypothesis is a statement that is testable based on observed data.
B. An alternative hypothesis is a statement of no difference between sample means
or proportions.
C. A hypothesis is a statement that may or may not be true, and it is developed for
testing.
D. An alternative hypothesis is a statement of the existence of a relationship or
difference between two measured phenomena.
For numbers 3-5, refer to the problem below.
An athletic trainer for women’s sprint has developed a new training program to improve
the running time in 100 m dash. It has been determined before that the mean running
time is 15 seconds.
3. How will you write the null hypothesis in symbols?
A. 𝜇 = 15
B. 𝜇 ≠ 15
C. 𝜇 < 15
D. 𝜇 > 15
4. Which of the following is the most appropriate alternative hypothesis?
A. The mean running time in a 100 m dash is equal to 15 seconds.
B. The mean running time in a 100 m dash is lesser than 15 seconds.
C. The mean running time in a 100 m dash is not equal to 15 seconds.
D. The mean running time in a 100 m dash is greater than 15 seconds.
5. What kind of test must be applied?
A. One-tailed test
B. Two-tailed test
C. It cannot be determined
D. Whether it’s a one-tailed or a two-tailed
test, it will give the same result.
4
6. Which of these alternative hypotheses is suited for a two-tailed test?
A. The height of papaya trees treated with compost fertilizer is taller than the standard
15 feet.
B. The number of calories for a serving of banana is unaffected whether it is latundan
or lacatan.
C. Ticket sales in MOA Arena for Season 81 UAAP Games are higher than the
Season 82 average of 20 000 tickets.
D. The amount of bad smoke coming from gasoline-fueled cars is higher than the
amount of bad smoke from diesel-fueled cars.
7. What is the level of significance for?
A. It leads the analyst to reject or not to reject the null hypothesis.
B. It refers to the range of values that leads to the rejection of the null hypothesis.
C. It is the probability of making the right decision to reject the null hypothesis when
it is incorrect.
D. It is a measure of the strength of the evidence present in the sample before
rejecting
the null
hypothesis and
concludes
that
the effect is
statistically
significant.
8. Which of the following best describes a Type I error?
A. When one decides to reject the null hypothesis when it is true.
B. When one decides not to reject the null hypothesis when it is true.
C. When one decides to reject the null hypothesis after found to be false.
D. When one decides not to reject the null hypothesis though it is found to be false.
9. Refer to the choices in number 8. Which of those is/are the correct decision/s?
A. A only
B. A & B
C. B & C
D. B, C & D
10. Who among these researchers has made the correct decision?
A. Mr. Co concluded that the social networking site Weverse is better than VLive
when in fact, it is no better.
B. Ms. Nakeeta rejected the null hypothesis; the mean height of Cluster S has no
difference to that of Cluster Z, when in fact, it has.
C. Mr. Nahk failed to reject the null hypothesis, and it was found out later that there
was not enough evidence to support the alternative hypothesis.
D. Both B and C
5
Lesson
1
UNDERSTANDING HYPOTHESIS
TESTING
What’s In
While browsing the internet, Mika came across a news page about the World Health
Organization (WHO) vaccination rollout in its fight against COVID-19. She saw this photo of
the comparison (set in percentages) of the effectiveness of the different COVID-19 vaccines
available as of February 2021.
Photo is taken from https://www.statista.com/chart/23510/estimated-effectiveness-of-covid-19-vaccine-candidates/
Figure 1. The estimated effectiveness of the COVID-19 vaccines from late-stage
clinical trials.
She became interested as to how the different manufacturers arrived at these
conclusions. She then thought of a question, “What were the fundamental assumptions used
by the manufacturers?”.
6
What’s New
To answer the question, “What were the fundamental assumptions used by the
manufacturers?” this lesson will discuss the important topics in hypothesis testing like
hypothesis, level of significance, types of errors in hypothesis testing, and rejection region.
Additionally, probabilities of committing Type I and Type II errors will also be introduced.
Figure 2. A wordle consisting of keywords and terms that you will learn from this module.
In conducting statistical studies, researchers always start with what they wish to
investigate. They postulate or conjecture something about the population. This conjecture is
put in the form of a statistical hypothesis.
What Is It
What is a statistical hypothesis?
A statistical hypothesis is a statement regarding an unknown population parameter. It
may or may not be true, and it is developed for testing. There are two types of hypotheses: the
null hypothesis and the alternative hypothesis.
1. The null hypothesis, denoted by 𝑯𝒐 , is a statement of no difference between sample
means or proportions and population means. It represents what the researcher doubts to
be true. It is the hypothesis that is either rejected or not rejected.
2. The alternative hypothesis, denoted by 𝑯𝟏 , is a claim that is contradictory to 𝐻𝑜 . It is an
operational statement of the conjecture that the researcher believes to be true and wishes
to investigate. It is what we conclude when we reject 𝐻𝑜 .
7
Mathematical Symbols Used in 𝑯𝒐 and 𝑯𝟏 :
𝑯𝒐
𝑯𝟏
not equal (≠)
equal (=)
less than (<)
more than (>)
Note!! 𝑯𝒐 is usually stated using the equal sign “=” since when we test 𝑯𝒐 the assumption
is that the parameter being tested is equal to a given specific value. Meanwhile, 𝑯𝟏
is usually stated in “≠”, “<” or “>” signs since it is considered as contradictory to the
𝑯𝒐 .
Illustrative Examples:
Directions. Identify whether the given statement is a null hypothesis or an alternative
hypothesis. Explain your answer.
1.
There is a significant difference in the academic performances of Grade 11-Gold and
Grade 11-Silver students during the school year 2020-2021.
Answer:
This is an alternative hypothesis because it states a difference in the academic
performances of the two groups of students.
2.
Grades in school do not predict a student’s success in the future.
Answer:
This is a null hypothesis since it states no relationship between school grades and future
success.
3.
The average height of the male members in Team Mudo is shorter than the average
height of the male members in Team Muli.
Answer:
This is an example of an alternative hypothesis because it states a difference in the
average height of the male members in each team. In this case, one team’s average
height is shorter than the other.
4.
The number of calories for a serving of banana is unaffected whether it is latundan or
lacatan.
Answer:
This is an example of a null hypothesis since it states that there is no relationship
between the kind of banana to its calorie content. The keyword is ‘unaffected.’
8
Here are illustrations of null and alternative hypotheses derived from real-life problems.
Directions: Write the appropriate null and alternative hypotheses in each problem.
5. A generic brand of antihistamine drug markets a capsule with a 50 mL dose. The
manufacturer is worried that the machine that fills the capsules has come out of calibration
and is no longer creating capsules with the appropriate dosage.
In words,
In symbols,
The machine did not come out of
calibration and still filling the 𝑯𝒐 : The dosage on the antihistamine 𝑯𝒐 : 𝜇 = 50
capsule is equal to 50 mL.
capsules with a 50 mL dose
The machine came out of
calibration and is not filling the 𝑯𝟏 : The dosage on the antihistamine
𝑯𝟏 : 𝜇 ≠ 50
capsules with 50 mL doses
capsule is not equal to 50 mL.
anymore.
6. A social scientist proposed that playing soft music during a test will favorably change the
test result. In the past, the mean test score was 73.
In words,
In
symbols,
The test result will still be the same
whether they do or do not play soft 𝑯𝒐 : The mean test score is equal to 73.
𝑯𝒐 : 𝜇 = 73
music during the test.
The result will be relatively better if
they play soft music during the test. 𝑯𝟏 : The mean test score is greater than
𝑯𝟏 : 𝜇 > 73
(”favorably” indicates higher mean
73.
score)
What is Hypothesis Testing?
Hypothesis testing is a statistical method used in making statistical decisions using
experimental data. It is an assumption that we make about the population parameter. The
methodology employed by the statistician depends on the nature of the data used and the
reason for the analysis.
Since the null and alternative hypotheses are contradictory, you must examine evidence
to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in
the form of sample data.
After you have determined which hypothesis the sample supports, you make
a decision. There are two options for a decision. They are “reject 𝐻𝑜 ” if the sample information
favors the alternative hypothesis or “do not reject 𝐻𝑜 ” or “fail to reject 𝐻𝑜 ” if the sample
information is insufficient to reject the null hypothesis.
We do not “accept the null hypothesis” because we don’t have all the data about the
population. Instead, we make use of a sample that represents the characteristics of the
population. Thus, the sample does not provide enough evidence to reject the null hypothesis,
but that does not prove that the null hypothesis is true. There is still a lot of data about the
9
population we do not have, so the null hypothesis could still be wrong; hence, we say “fail to
reject.” Failing to reject a hypothesis should not be confused with acceptance.
Other Important Definitions:
A statistical test is done to decide whether the null hypothesis should be rejected or not. The
numerical value obtained from a statistical test is called the test statistic.
Level of significance refers to the degree of significance in which we accept or reject the null
hypothesis. It is a measure of the strength of the evidence present in the sample before
rejecting the null hypothesis and concludes that the effect is statistically significant.
100% accuracy is not possible for accepting or rejecting a hypothesis, so we therefore
select a level of significance that is usually 5% or 0.05.
Rejection Region (RR), also known as the critical region, refers to the range of values that
leads the statistician to reject the null hypothesis. On the other hand, the non-rejection region
(NRR) is the set of values of the test statistic for which the null hypothesis is not rejected.
One-tailed test. A test of statistical hypothesis where the region of rejection is on one side
only of the sampling distribution.
Two-tailed test. A test where the region of rejection is on both sides of the sampling
distribution.
The alternative hypothesis dictates whether a particular test is a one-tailed or two-tailed
test. Alternative hypotheses that are stated using the ≠ sign imply two-tailed tests.
Alternative hypotheses that are stated using the < or > sign imply one-tailed tests.
These are illustrations of a two-tailed test and a one-tailed test.
*Two-tailed test
Figure 3. A two-tailed test is designed to show whether the mean of a sample is significantly
greater than and significantly less than the mean of a population.
10
*Negative one-tailed test
*Positive one-tailed test
Photos are taken from http://sciences.usca.edu/biology/zelmer/305/hypo/tails/
Legend:
Rejection region (RR)
Non-rejection region (NRR)
Figure 4a and 4b. A one-tailed test is a test in which the critical area of a distribution is onesided so that it is either greater than or less than the mean of a population, but not both.
Types of Errors in Hypothesis Testing
1. Type I Error is the error of rejecting the null hypothesis when it is true. Type I error is
denoted by alpha (𝜶). In hypothesis testing, the normal curve that shows the critical region
is called the alpha region. The significance level predetermines the probability of committing
a Type I error in hypothesis testing.
2. Type II Error is the error committed when we decide not to reject the null hypothesis when
in fact, it is false. Type II error is denoted by beta (𝜷). In hypothesis testing, the normal
curve that shows the acceptance region is called the beta region. The probability of not
committing a Type II error is called the power of the test, and it is equal to 1 − 𝛽. The
power of the test is the probability that we make the right decision when the null hypothesis
is not correct; we rightly reject it.
There are four possible outcomes when testing a statistical hypothesis.
𝑯𝒐 is true
𝑯𝒐 is false
Fail to reject 𝑯𝒐
Correct decision
Type II error (𝛽)
Reject 𝑯𝒐
Type I error (𝛼)
Correct decision
11
Illustrative Examples:
Directions: Identify whether the decision is correct or not. If it is not correct, identify whether
the error is a Type I or a Type II error.
1. 𝐻𝑜 is true and we fail to reject it.
Answer: It is a correct decision.
𝐻𝑜 is true
𝐻𝑜 is false
Fail to reject 𝐻𝑜
Correct decision
Type II error (𝛽)
Reject 𝐻𝑜
Type I error (𝛼)
Correct decision
2. 𝐻𝑜 was rejected and it was found out to be false.
Answer: It is a correct decision.
𝐻𝑜 is true
𝐻𝑜 is false
Fail to reject 𝐻𝑜
Correct decision
Type II error (𝛽)
Reject 𝐻𝑜
Type I error (𝛼)
Correct decision
3. 𝐻𝑜 was rejected and it was found out to be true.
Answer: It is not a correct decision. A Type I error (α) was committed.
𝐻𝑜 is true
𝐻𝑜 is false
Fail to reject 𝐻𝑜
Correct decision
Type II error (𝛽)
Reject 𝐻𝑜
Type I error (𝜶)
Correct decision
4. 𝐻𝑜 is false and we fail to reject it.
Answer: It is not a correct decision. A Type II error (β) was committed.
𝐻𝑜 is true
𝐻𝑜 is false
Fail to reject 𝐻𝑜
Correct decision
Type II error (𝜷)
Reject 𝐻𝑜
Type I error (𝛼)
Correct decision
Statistical Decision for Hypothesis Testing
In statistical analysis, we have to make decisions about the hypothesis. These decisions
include deciding if we should reject the null hypothesis or if we should decline to reject the null
hypothesis. If the test statistic falls within the rejection region, the decision is to reject the null
hypothesis; otherwise, decline to reject the null hypothesis. The critical values separate the
rejection region from the non-rejection region. This method of making decisions in a statistical
study is called the critical value approach.
Another way of making decisions in a statistical study is through the use of the
probability value (written as 𝑝 − 𝑣𝑎𝑙𝑢𝑒). The rule is: if the 𝑝 − 𝑣𝑎𝑙𝑢𝑒 is less than the
significance level, we reject the null hypothesis; otherwise, do not reject the null hypothesis.
12
What’s More
ACTIVITY 1. Hype Up Your Hypothesis!
Directions: Determine whether each statement is a null or an alternative hypothesis. Explain
your answer in 1-2 sentences. If it is an alternative hypothesis, determine if it is
one-tailed or two-tailed.
1. The amount of radiation a desktop computer emits has no difference to that of a
cellphone.
____________________________________________________________________
__________________________________________________________________
2. The validity of passports in other countries is shorter than the validity of passports
issued in the Philippines.
____________________________________________________________________
__________________________________________________________________
3. Korean music and industry are gaining more popularity than Western music nowadays.
____________________________________________________________________
__________________________________________________________________
ACTIVITY 2. Guess My Type!
Directions: Provide an explanation for the situations below.
1. The researcher failed to reject the null hypothesis, and it was found
out later that there was not enough evidence to support the
alternative hypothesis. Was this a correct decision?
____________________________________________________
____________________________________________________
____________________________________________________
2. It was concluded that the social networking site
Facegram is better than Instabook when in fact, it is no
better. What Type of error was committed?
__________________________________________
__________________________________________
__________________________________________
13
What I Have Learned
•
A statistical hypothesis is a statement regarding an unknown population parameter. It
may or may not be true, and it is developed for testing. There are two types of hypothesis,
namely:
a. Null hypothesis (𝑯𝒐 ) is a statement of no difference between sample means or
proportions and population means. It is the hypothesis that is either rejected or not
rejected.
b. Alternative hypothesis (𝑯𝟏 ) is a claim that is contradictory to 𝐻𝑜 . It is what we
conclude when we reject 𝐻𝑜 .
•
Hypothesis testing is a statistical method used in making statistical decisions using
experimental data. There are two types of errors committed in hypothesis testing: Type
I error or Type II error.
a. Type I Error is the error of rejecting the null hypothesis when in fact, it is
true. Type I error is denoted by alpha (𝜶).
b. Type II Error is the error of failing to reject the null hypothesis when it is
false. Type II error is denoted by beta (𝜷).
•
In statistical analysis, we have to make decisions about the hypothesis. These
decisions include deciding if we should reject the null hypothesis or if we should
decline to reject the null hypothesis.
14
Lesson
2
UNDERSTANDING MORE
ELEMENTS IN HYPOTHESIS
TESTING
What’s In
What does the photo on the right depict?
___ ___ ___ ___ ___ ___ ___
Hint: It is defined as a method that is used in making
decisions using experimental data.
Photo is taken from https://4-pics-1word.com/4-pics-1-word-cheats-4-letters/4pics-1-word-blood-pressure-doctor/
What’s New
Testing is done to prove that a claim is true or not. If we explore the results of a carefully
designed experiment that has already been analyzed to a defined population, then we are
making a statistical inference. Such inference involves, among other aspects, statistical
decision that certain population differs with respect to a measured variable.
What Is It
Identifying the Parameter to be Tested Given a Real-life Problem
Illustrative Examples:
1. WTFood Inc. is claiming that their baking time for quick-to-bake ready mix pies (product A)
is less than the average for a similar product (product B). Jan Miranda, a cooking guru,
and food vlogger, has been offered by the company to advertise product A. To her
experience, she has been doing the same stuff for years, and it takes her 10 minutes to
bake a pie. She wishes to make sure that the claim of the company is true before she
accepts the offer.
Let us help Jan Miranda by formulating statistical hypotheses.
15
Let us consider three possible scenarios.
Scenario 1:
Jan Miranda would like to find out if there is a difference between the mean baking time
of the quick-to-bake ready-mix pie (product A) and the mean baking time of a similar product
(product B). We can represent our null and alternative hypotheses as follows:
In words,
In symbols,
𝑯𝒐 : The mean baking time for quick-to-bake ready-mix pies
𝑯𝒐 : 𝜇 = 10
(product A) is 10 minutes.
𝑯𝟏 : The mean baking time for quick-to-bake ready-mix pies
𝑯𝟏 : 𝜇 ≠ 10
(product A) is not 10 minutes.
If 𝜇 ≠ 10, then it can mean either 𝜇 > 10 or 𝜇 < 10, and both cases should be
considered when we make our decision. Since the alternative hypothesis is two-sided or nondirectional, then this is a two-tailed test.
Scenario 2:
Jan Miranda would like to determine if the mean baking time of the quick-to-bake readymix pies (product A) is less than the mean baking time of a similar product (product B). We
can represent our null and alternative hypotheses as follows:
In words,
In symbols,
𝑯𝒐 : The mean baking time for quick-to-bake ready-mix pies
𝑯𝒐 : 𝜇 = 10
(product A) is 10 minutes.
𝑯𝟏 : The mean baking time for quick-to-bake ready-mix pies
𝑯𝟏 : 𝜇 < 10
(product A) is less than 10 minutes.
Since the alternative hypothesis is one-sided or one-directional, then this is a one-tailed
test. Likewise, the alternative hypothesis represents what the company is claiming; that is, the
mean baking time is less than the known value.
Scenario 3:
Jan Miranda would like to determine if the mean baking time of the quick-to-bake readymix pies (product A) is greater than the mean baking time of a similar product (product B). We
can represent our null and alternative hypotheses as follows:
In words,
In symbols,
𝑯𝒐 : The mean baking time for quick-to-bake ready-mix pies
𝑯𝒐 : 𝜇 = 10
(product A) is 10 minutes.
𝑯𝟏 : The mean baking time for quick-to-bake ready-mix pies
𝑯𝟏 : 𝜇 > 10
(product A) is greater than 10 minutes.
16
This also a one-tailed test since the alternative hypothesis is one-sided or onedirectional. The alternative hypothesis represents the case wherein the mean baking time is
greater than the known value.
Question: Which of the three scenarios would be most appropriate in Jan Miranda’s
case?
Answer: Since she wants to verify if indeed the mean baking time of the product is less
than a known value, then Scenario 2 would be the most appropriate for Jan
Miranda’s concern.
___
2. The Department of Health (DOH) would like to determine if exposure of pregnant women
to electronic devices tends to adversely affect the size of the head circumference of
newborn babies. It is known that the mean head circumference of a newborn is 35 cm.
Let the random variable be the head circumference of a newborn.
As stated in the problem, we can have the null hypothesis as 𝜇 = 35. However, there
is no explicit mention of the alternative hypothesis; what is stated is that there is a
tendency to affect newborn babies’ head circumference adversely. The “adverse effect”
implies that the head circumference is statistically different from the known mean of 35
cm. Thus, we can conclude that this is a two-tailed test and that our alternative hypothesis
is 𝜇 ≠ 35.
In words,
𝑯𝒐 : The mean head circumference of newborn babies is
35 cm.
𝑯𝟏 : The mean head circumference of newborn babies is
not 35 cm.
3.
In symbols,
𝑯𝒐 : 𝜇 = 35
𝑯𝟏 : 𝜇 ≠ 35
In a production line for computer external hard drives, the quality control engineer
hypothesizes that the number of defects can be optimized during the manufacturing
process if robots are used instead of human beings. Currently, the mean number of
defective drives per 1000 is 12.
The random variable here is the number of defectives per 1000 units produced during the
manufacturing process if robots are used instead of human beings.
From the problem, we can easily write our null hypothesis; it is 𝜇 = 0.012 (from 12 in
1000 or
12
).
1000
Note that the term “optimum” means the most favorable outcome. Hence,
in a production line wherein we are talking of the number of defects, the “most favorable
outcome” would be to have the number of defects less than the known value. Thus, our
alternative hypothesis is 𝜇 < 0.012.
In words,
In symbols,
𝑯𝒐 : The mean number of defectives produced during the
manufacturing process if robots were to be used instead 𝑯𝒐 : 𝜇 = 0.012
of human beings is 12 per 1000 units.
17
𝑯𝟏 : The mean number of defectives produced during the
manufacturing process if robots were to be used instead 𝑯𝟏 : 𝜇 < 0.012
of human beings is lesser than 12 per 1000 units.
What’s More
ACTIVITY 3. Don’t You Ever Miss!
Directions: Supply the missing term/s in the paragraph below.
A (1)_________________ is a statement regarding an unknown population parameter.
It is developed for the purpose of (2)__________________. There are two types of (your
answer in no. 1), the (3)________________________ and the (4)______________________.
A hypothesis is subject to testing called (5)________________________. It is a
method that is used to arrive at sound decisions. In this method, there two types of error that
a researcher may commit. (6)_____________ is the error of rejecting the null hypothesis when
it is true while (7)____________ is the error of not rejecting the null hypothesis when it is false.
•
What I Can Do
Activity 4. Hypothesis Pa More!
Directions: For each of the following, identify the random variable/s and formulate the null
and alternative hypotheses (in words and symbols).
1. The federation of private school teachers has developed a
new evaluation instrument that they claim has higher
reliability by producing less error in evaluation. In the past, the
mean number of errors in the evaluation was 20%.
𝐻0 : ____________________________________________
𝐻1 : ____________________________________________
Photo is taken from https://www.routledge.com/Handbookon-Teacher-Evaluation-with-CD-ROM/StrongeTucker/p/book/9781930556584
2. In an advertisement, a certain brand of shampoo is claiming that
the use of this product will make the hair grow faster. It is known
that the mean length of growing hair over thirty days is 2 cm
.
𝐻0 : ____________________________________________
𝐻1 : ____________________________________________
Photo is taken from https://stylecaster.com/beauty/besthair-growth-shampoos/
18
ACTIVITY 5. Feed Me... Meow~
Directions: Do what is asked. Write your answer on a separate sheet of paper.
1. Jam, a cat lover, has five pet cats at home. She feeds them
organic cat food because she claims that feeding the cats
with cat food had an impact on the cats’ lifespan. According
to a study, the mean lifespan of cats is 12 years.
a. State the null hypothesis (in words and symbols)
b. State the alternative hypothesis (in words and symbols)
c. Is the test one-tailed or two-tailed? Explain in 1-2
sentences.
Photo is taken from https://www.123rf.com/photo_25246690_funnychild-boy-feeding-cats-kittens.html
For item d, use the decision below as your reference.
The null hypothesis was not rejected, and it was found out later that feeding cats with
organic food do not impact a cat’s lifespan.
d. Explain whether the decision was correct or not.
2. Use the photo on the right as your reference.
a. Formulate a null hypothesis (in words and in
symbols).
b. Formulate an alternative hypothesis (in words and in
symbols).
c. Is the test one-tailed or two-tailed? Explain in 1-2
sentences.
d. Identify the parameter to be tested.
Photo is taken from https://open.spotify.com/album/2QOB3wEL7prrvbWfZoMMkv
19
Assessment
Directions: Read the questions carefully, then choose the best answer from the given choices.
1. Which of the following does not describe hypothesis testing?
A. It is a test of an educated guess to verify conclusions.
B. It is a statistical method that is used in making decisions.
C. It is the examination of the pieces of evidence to prove or disprove an argument.
D. It is a test of the pieces of evidence to pronounce whether an argument is true or
false.
2. Which of the following statements is true?
A. A hypothesis is a non-testable statement and is only used for arguments.
B. An alternative hypothesis is a statement of no difference between sample means
or proportions.
C. A hypothesis is a statement that may or may not be true, and it is developed for
the purpose of testing.
D. A null hypothesis is a statement of the existence of a relationship or difference
between two measured phenomena.
For numbers 3-5, refer to the problem below.
An athletic trainer for men’s hurdle race has developed a new training program to
improve the running time in the standard long hurdle race. It has been determined before
that the mean running time is 48 seconds.
3. How will you write the null hypothesis in symbols?
A. 𝜇 = 48
B. 𝜇 ≠ 48
C. 𝜇 < 48
D. 𝜇 > 48
4. How will you write the alternative hypothesis in symbols?
A. 𝜇 = 48
B. 𝜇 ≠ 48
C. 𝜇 > 48
D. 𝜇 < 48
5. What kind of test must be applied?
A. One-tailed test
B. Two-tailed test
C. It cannot be determined
D. Whether it’s a one-tailed or a two-tailed test, it will give the same result
6. Which of the following best describes a Type II error?
A. When one decides to reject the null hypothesis when it is true.
B. When one decides not to reject the null hypothesis when it is true.
C. When one decides to reject the null hypothesis after found to be false.
D. When one decides not to reject the null hypothesis though it is found to be false.
20
7. Refer to the choices in number 6. Which of those is/are the correct decision/s?
A. A only
B. A & B
C. B & C
D. B, C & D
8. What is the level of significance for?
A. It leads the statistician to reject or not to reject the null hypothesis.
B. It refers to the range of values that leads to the rejection of the null hypothesis.
C. It is the probability of making the right decision to reject the null hypothesis when
it is incorrect.
D. It is a measure of the strength of the evidence that must be present in
the sample before rejecting the null hypothesis and conclude that the effect is
statistically significant.
9. Which of these alternative hypotheses is suited for a two-tailed test?
A. The height of papaya trees treated with compost fertilizer is taller than the standard
15 feet.
B. The number of calories for a serving of banana is unaffected whether it is latundan
or lacatan.
C. Ticket sales in MOA Arena for Season 81 UAAP Games are higher than the
Season 82 average of 20 000 tickets.
D. The amount of bad smoke coming from gasoline-fueled cars is higher than the
amount of bad smoke from diesel-fueled cars.
10. Who among these researchers has made a mistake in decision-making?
A. Ms. Cua concluded that the social networking site Weverse is better than VLive
when in fact, it is no better.
B. Mr. Gonzalez rejected the null hypothesis, the mean height of Cluster S has no
difference to that of Cluster Z, when in fact, it has.
C. Mr. Nam failed to reject the null hypothesis, and it was found out later that there
was enough evidence to support the alternative hypothesis.
D. All of the above
21
Answer Key
22
References
Arceo, Virginia R., et.al. Math in Today’s World Statistics and Probability. Phoenix Publishing
House. Quezon City, 2018.
“How Effective Are The COVID-19 Vaccines?”, Niall McCarthy. Accessed March 19, 2021.
https://www.statista.com/chart/23510/estimated-effectiveness-of-covid-19-vaccinecandidates/
“Hypothesis
Testing”,
Course
Hero.
Accessed
March
19,
2021.
https://www.coursehero.com/file/p7befb78/HYPOTHESIS-TESTING-Hypothesis-testing-is-astatistical-method-that-is-used-in/
“Hypothesis”,
Course
Hero.
Accessed
March
https://www.coursehero.com/file/88449964/HYPOTHESISdocx/
19,
2021.
“Introductory Statistics”,
Open Stax
College. Accessed
March
20,
https://opentextbc.ca/introstatopenstax/chapter/null-and-alternative-hypotheses/
2021
“Hypothesis
Testing”,
Christina
Majaski.
Accessed
https://www.investopedia.com/terms/h/hypothesistesting.asp
2021.
March
20,
“Hypothesis
Testing”,
Statistics
Solutions.
(2013).
Retrieved
from https://www.statisticssolutions.com/academic-solutions/resources/directory-ofstatistical-analyses/hypothesis-testing/
Accessed
March
21,
2021.
https://www.statisticssolutions.com/hypothesis-testing/
“Setting the Hypotheses”, Penn State Eberly College of Science. Accessed March 21, 2021
https://online.stat.psu.edu/stat100/lesson/10/10.1
“One- and Two-Tailed Tests”, Derek Zelmer.
http://sciences.usca.edu/biology/zelmer/305/hypo/tails/
Accessed
March
21,
2021
“Failing to Reject the Null Hypothesis”, Jim Frost. Accessed April 30, 2021
https://statisticsbyjim.com/hypothesis-testing/failing-reject-nullhypothesis/#:~:text=Failing%20to%20reject%20the%20null%20indicates%20that%20our%2
0sample%20did,leads%20to%20the%20convoluted%20wording!
“What ‘Fail to Reject’ Means in a Hypothesis Test”, Courtney Taylor. Accessed May 1, 2021
https://www.thoughtco.com/fail-to-reject-in-a-hypothesis-test-3126424
”Two-Tailed
Test”,
Adam
Hayes.
Accessed
https://www.investopedia.com/terms/t/two-tailed-test.asp
”One-Tailed
Test”,
Will
Kenton.
Accessed
https://www.investopedia.com/terms/o/one-tailed-test.asp
May
on
May
2,
2,
2021
2021
23
For inquiries or feedback, please write or call:
Department of Education – Schools Division of Laoag City
Curriculum Implementation Division (CID)
Brgy. 23 San Matias, Laoag City 2900
Contact Number: (077) 771-3678
Email Address: laoag.city@deped.gov.ph