Formulating Null and Alternative Hypotheses

FORMULATING APPROPRIATE NULL
AND ALTERNATIVE HYPOTHESES
ON A POPULATION MEAN

EVELYN P. PELAEZ
Teacher III

LET US PRAY

CHECKING OF
ATTENDANCE

CLASSROOM RULES:

1. Raise your hand if you want to

answer.

2. No using of cellphones
3. If there are LGBTQ member. Let us
Respect each other opinions or ideas.

OBJECTIVES:

1. Identify the notation to be used in
formulating Hypotheses.
2. Formulates the appropriate null and
alternative hypotheses on a population
mean. M11/12SP-IVb-1

Activity 1. NO MORE NO LESS! Using Quizziz.

Which of the given equality/inequality expressions describes each situation? Select the best answer.

Multiple Choice

1. The survey shows that the number of students (n) who have parents with a house of their own is less than 20.

• 𝑛<20          

• 𝑛>20       

• 𝑛≤20            

• 𝑛≥20

Multiple Choice

2. Mother gives me at most P200 allowance (n) in a week.

• 𝑛≥200            

• 𝑛≤200

• 𝑛>200

• 𝑛<200

Multiple Choice

3. Larry is an industrious appliance salesman. His average sales (n) in a week is at least P10, 000.

• 𝑛<10,000  

• 𝑛> 10,000

• 𝑛≤10,000

• 𝑛≥10,000

Multiple Choice

4. A son’s savings (n) is greater than P1,500.

• 𝑛=1,500

• 𝑛≠ 1,500

• 𝑛> 1,500

• 𝑛≥ 1,500

Multiple Choice

5. Marco’s salary (n) is equal to P20, 000.

• 𝑛= 20,000

• 𝑛≠20,000   

• 𝑛≤ 20,000

• 𝑛<20,000

To formulate our life. What is your favorite phrases in Life?

ACTIVITY 2
HYPOTHESIS-TESTING COMMON PHRASES

RULES:

1.Divide students into 6 groups.

2.The groups roll a die to determine which
number to receive with a symbol on it. This will

will also be the line-up to present.

3.Each group receives a symbol, and they will

have to find the correct phrases and match the phrase with the correct symbols.

RULES:

5.The group will be graded according to rubrics.

4. After matching the phrases with the correct symbols. Then, think of strategies that make it easier to remember.
Ex. poem, song

RUBRICS.....
5 POINTS : The solution and answers are correct; with correct interpretation.

The presentation is clear, and the group clearly worked together with each team making an important contribution in the output.

RUBRICS.....
4 POINTS : The solution is somewhat correct, but the answers are correct with correct interpretation.

The presentation is somewhat clear, and the group worked together.

RUBRICS.....
3 POINTS : The solution is somewhat correct. Some of the answers and interpretation are correct.

The presentation is somewhat clear, and some of members are worked together.

RUBRICS.....
2 POINTS : The solution is partly correct but the answers and interpretation are incorrect.

The presentation is partly clear, but the group are not worked together.

RUBRICS.....
1 POINT : The solution is not clear. The answers and interpretation are incorrect.

The presentation is not clear. The group are not worked together.

SYMBOLS

=

<

≠

≤

>

≥

has not changed from
is not equal to
is increased
is decreased
is at least
is not more than
is at most
is not less than
is the same as
is not the same
is greater than
is less than
is not less than
is not more than

is equal to
is different from
is exactly the same as
has changed from
is higher than
is above
is lower than
is below
is greater than or equal to
is less than or equal to
is bigger than
is smaller than
is longer than
is decreased or reduced from
is more than
is not more than

Open Ended

WHAT ARE THE COMMON PHRASES TO THE FOLLOWING SYMBOLS:

1. (=) 2. (≠) 3. (>) 4. (<) 5. (≤) 6. (≥)

A STATISTICAL HYPOTHESIS IS A
STATEMENT ABOUT A PARAMETER
AND DEALS WITH EVALUATING THE
VALUE OF PARAMETER.

Null Hypothesis (	Alternative Hypothesis (
It states that there is no difference between population parameters (such as mean, standard deviation, and so on) and the hypothesized value.	It states that the population parameter has some statistical significance (smaller, greater, or different than) with the hypothesized value.
There is no observed effect.	There is an observed effect.

TO STATE THE NULL AND ALTERNATIVE HYPOTHESES
CORRECTLY:

1.Identify the parameter in a given

problem.

2.Identify the claim to be tested that may

show up in null or alternative hypothesis.

3.Translate the claim into Mathematical

symbols/ notations.

TO STATE THE NULL AND ALTERNATIVE HYPOTHESES
CORRECTLY:

4. Formulate first the null hypothesis (𝐻𝑜) then
alternative hypothesis (𝐻𝑎) based on the three
different ways in writing hypothesis as illustrated
below:
𝑯𝒐: μ=𝒌

𝑯𝒐: μ≤𝒌

𝑯𝒐: μ≥𝒌

𝑯𝒂: μ≠𝒌

𝑯𝒂: μ>𝒌

𝑯𝒂: μ<𝒌

LET US TAKE AN EXAMPLE FROM YOUR
PREVIOUS ACTIVITY.

Larry is an industrious Appliance salesman. His average sales (n) in a week is greater than P 10,000.

SOLUTION:
THE PARAMETER IS THE AVERAGE SALES (n) IN A WEEK.THE CLAIM USED THE
WORD “GREATER THAN” WHICH AS SEEN IN THE TABLE
ABOVE, CORRESPONDS TO
THE SYMBOL (>).
THEREFORE, THE ANSWER IS
n>10000.

NOTE:
𝐻𝑜: ALWAYS HAS = SYMBOL IN IT.
𝐻𝑎: NEVER HAS AN = SYMBOL IN IT.
THE CHOICE OF SYMBOL DEPENDS ON THE WORDING
OF THE HYPOTHESIS TEST. HOWEVER, BE AWARE THAT
MANY RESEARCHERS USE = (EQUAL SIGN) IN THE NULL
HYPOTHESIS, EVEN WITH > OR < AS THE SYMBOL IN THE
ALTERNATIVE HYPOTHESIS. NOTICE ALSO THAT THE
NOTATION OF ALTERNATIVE HYPOTHESIS
COMPLEMENTS THE NULL HYPOTHESIS

ILLUSTRATIVE EXAMPLES:

The average weight of all Grade
11 students in Senior High
School is 169cm.

Solution:
First, identify the parameter which is the average
weight of all Grade 11 students.
Since it is a population mean, use the notation 𝝁.
The claim in this example is that
the average weight is 169 cm which translates to 𝝁=𝟏𝟔𝟗
and is considered as null hypothesis.

To formulate the alternative hypothesis, write the
complement/opposite of the null hypothesis which is
the average weight is not equal to 169 cm.

𝑯𝒐: THE AVERAGE WEIGHT OF ALL
GRADE 11 STUDENTS IS 169 CM.
𝑯𝑶:𝝁=𝟏𝟔𝟗 (CLAIM)

𝑯𝒂: THE AVERAGE WEIGHT OF ALL
GRADE 11 STUDENTS IS NOT 169 CM.
𝑯𝒂: 𝝁≠𝟏𝟔𝟗

The ALTERNATIVE HYPOTHESIS can take another form depending on the value of the Parameter. The Parameter may increase, decrease or changed from the null value.

ONE-TAILED AND
TWO-TAILED TEST

ONE-TAILED AND
TWO-TAILED TEST

IT'S YOUR TURN!


MATH TRAIL

RULES:
1. The MATH TRAIL has 4 Stations.
2. Each Group will stay in a station for an allotted time (2minutes) to finish the task in every station.
3. The 2 teams allowed to be in one station. In the event if the group has finished early the alotted time,then it can go to another station.

RULES:
4. As soon as the group finishes the station, the teams will submit their paper immediately to the Station Commander and it is graded according to rubrics.

Station 1. Fill Me!
Station 2. Let's Hypothesize

Station 3. One-Tailed or Two - Tailed!
Station 4. Formu-Tail

ASSESSMENT:
Directions: Formulate the Null and Alternative Hypothesis,
The average price of a certain type of car is greater than P600,000.

APPLICATION:
Based on the activity.
Why do we need to determine Hypothesis testing common phrases?
How to formulate Null and alternative hypotheses?
How can you relate the activity in real life situation like dealing to the indigenous people?

GENERALIZATION:

WHAT ARE THE COMMON PHRASES USE IN HYPOTHESIS TESTING? IDENTIFY THE THREE DIFFERENT WAYS IN WRITING HYPOTHESIS? AND THE DIRECTIONAL TEST? HOW TO FORMULATE NULL AND ALTERNATIVE HYPOTHESIS?

EVALUATION: A.Direction: Complete the following statements. 1. __________________ is a statement about a parameter and deals with evaluating the value of parameter. 2. The two kinds of hypothesis are________and____________. 3. To formulate a hypothesis, the steps are: a. ________________________ b. _____________________ c. ________________________ d. ________________________ 4. The test of hypothesis can be ___________ if the alternative hypothesis uses ≠ symbol or __________________ if it uses <𝑜𝑟 > symbols. 5. The null hypothesis and alternative hypothesis can be denoted as ______ and ______, respectively.

EVALUATION:  B.Formulate the Null and Alternative Hypothesis A research organization reports that the mean of adult grocery shoppers who never buy the store brand in Metro Manila is 300.

𝐻𝑜: _________________ 𝐻𝑎: _________________ _______- tailed test  

ASSIGNMENT:
Project SIM
Cite five(5) research questions used in real life and formulate your Null and Alternative Hypothesis.