HYPOTHESIS

TESTING
 WHAT IS HYPOTHESIS
TESTING? NOTE:
Hypothesis testing isn't a
random guess. It follows a
structured approach with
Hypothesis testing is a systematic
well-defined steps to
procedure for deciding whether the
ensure consistency and
results of a research study support a
reliability.
particular theory which applies to a
population. Hypothesis testing uses
sample data to evaluate a hypothesis
about a population.
 TWO TYPES OF HYPOTHESIS
TESTING
01. 02.
Null Alternative
hypothesis Hypothesis
 NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS

the hypothesis that there is no HYPOTHESIS An alternative

TESTING
significant difference between
specified populations, any observed hypothesis is an
difference being due to sampling or
experimental error.
opposing theory to the
null hypothesis.

EXAMPLE
Null and Alternative Hypothesis Example: Exercise and Sleep Quality

Research Question: Does regular exercise improve sleep quality?

Null Hypothesis (H₀): There is no difference in sleep quality between people who exercise regularly and those who do not exercise
regularly.

This null hypothesis assumes that exercise has no impact on how well people sleep.

Alternative Hypothesis (H₁): People who exercise regularly have better sleep quality compared to those who do not exercise regularly.

This alternative hypothesis states the opposite of the null hypothesis and predicts that exercise does have a positive effect on sleep
quality.

additional illustrations on the following slide

TYPES OF
ERRORS
TYPES OF ERRORS

TYPE I ERROR
a type I error happens when you
reject a null hypothesis that's actually
true. Researchers set a level of
significance (alpha, denoted by α) to
control this risk. This means they
accept a small chance of making a
type I error.
TYPES OF ERRORS

TYPE II ERROR
a type II error happens when you
accept a null hypothesis that's
actually false. This can be because the
evidence isn't strong enough to reject
the null hypothesis. Beta (β)
represents the chance of making a
type II error.
ONE-TAILED
AND TWO-
TAILED TEST
ONE-TAILED AND TWO-TAILED TEST

ONE-TAILED TEST TWO-TAILED

the alternative hypothesis uses the TEST
symbols > or <. If the hypothesis the rejection region is on both sides of
contains the >, then the region of the curve. The alternative
rejection is on the right tail of the hypothesis contains the symbol ≠. The
curve. If it contains the < symbol, then critical region for rejection of the null
the region of rejection is on the left hypothesis is split between both tails of
tail of the curve. the sampling distribution.

NOTE: One-tailed tests are used when researchers have specific

directional hypotheses, while two-tailed tests are more appropriate
when researchers are simply interested in whether there is a
difference or relationship, regardless of direction.
 ONE-TAILED AND
TWO-TAILED TEST

SIGNIFICANCE LEVEL (a)

The probability of rejecting the null hypothesis when it is
actually true. Commonly chosen values for α are 0.05 (5%) and
0.01 (1%). It represents the threshold for deciding whether to
reject the null hypothesis. Also specifies the size of the
rejected region or critical region.

NOTE:
“In the Two-tailed test, alpha (α) is divided by 2 into both tails.
In one one-tailed test, it is not divided”
 ONE-TAILED AND
TWO-TAILED TEST

NOTE:
“In the Two-tailed test, alpha (α) is divided by 2 into both tails.
In one one-tailed test, it is not divided”
REJECTION REGION TEST STATISTIC
refers to the region where the A numerical value
value of the calculated from sample
statistic lies for which we will data that is used to
reject the null hypothesis.
determine whether to
This region is called a critical
region. On the other hand, the reject the null hypothesis.
non-rejection region (or The choice of test statistic
acceptance region) is the set depends on the specific
of all values of the test hypothesis test being
statistic that causes us to fail conducted.
to reject the null hypothesis.
PARAMETERS
WHAT ARE PARAMETERS?
Parameters are numerical quantities that
characterize a given population or some
aspect of it. They are used in statistical
analysis to describe the entire population,
as opposed to statistics, which are derived
from a sample of the population.
EXAMPLES
Common parameters include
measures of central tendency (like
mean, median, and mode) and
measures of spread (like standard
deviation and variance).
SYMBOLS:
USAGE IN HYPOTHESIS TESTING
Parameters are crucial in hypothesis testing,
where they are translated into symbols and
used to formulate null and alternative
hypotheses. For example, if a parameter is the
mean height of adult Filipinos, it could be
represented as ( μ= 163 ) cm in the null
hypothesis.
IMPORTANCE:
Understanding parameters is essential for
identifying the correct test statistic (like z-
test or t-test) and for making inferences
about the population based on sample data.
They help in determining how data behave on
average and how they are spread from the
central tendency.
EXAMPLES
 EXAMPLE 1
A teacher wishes to test if the
average GPA of students in the high
school is different from 2.7. State the
null and alternative hypotheses.
 EXAMPLE 2
A company manufactures car batteries with an average
lifespan of 2 or more years. An engineer believes this
value to be less. Using 10 samples, he measures the
average lifespan to be 1.8 years with a standard
deviation of 0.15.

(A) State the null and alternative hypothesis.

(B) At a 99% confidence level, is there enough evidence to
discard the null hypothesis?
(C) Illustrate the graph.
 EXAMPLE 3
A researcher wants to test if the average height of high
school students has increased in the past decade. They
collect a random sample of 27 students and find that the
sample mean height is 165 cm with a standard deviation of
5 cm. The population mean height 10 years ago was 160 cm.
The researcher believes that the increase in height is
significant and wants to perform a hypothesis test at a 5%
level of significance.

a) State the null and alternative hypotheses.

b) Calculate the test statistic.
c) Determine the critical value and make a decision about
the null hypothesis.
 EXAMPLE 4
Company XYZ manufactures calculators with an average
mass of 450g. An engineer believes that the average
weight to be different and decides to calculate the
average mass of 40 calculators and finds that the
average weight is 445g with a standard deviation of 3.

a. State the null and alternative hypotheses.

b. At 95% confidence level, is there enough evidence to discard
the null hypothesis?
c. Illustrate the graph.
d. State the appropriate conclusion.
 EXAMPLE 5
A factory has a machine that dispenses 80mL of fluid in
a bottle. An employee believes the average amount of
fluid is less than 80mL. Using 30 samples, he measures
the average amount dispensed by the machine to be
78mL with a standard deviation of 2.5.

(A) State the null and alternative hypothesis.

(B) At a 95% confidence level, is there enough evidence to
support the idea that the machine is not working properly?
(C) Illustrate the graph.
 EXAMPLE 6
An instructor gives his class an achievement test
which, as he knows from years of experience, yields
a mean u = 85 His present class of 25 obtains a
mean of 87 and a standard deviation of 5. He now
claims that his present class is a superior class. Is
he correct in his claim alpha = 0.05'

A.) Identify null/alternative hypothesis

B.) Calculate the test statistic
C.) Find the critical value
D.) Illustrate the graph.
 EXAMPLE 7
A manufacturer of cellular laptop batteries claims that when
fully charged, the mean life of his products lasts for 26 hours.
Mr. Smith, a regular distributor, disagrees and randomly picked
and tested 27 of the batteries. His test showed that the average
life of his sample is 24.3 hours with a standard deviation of 5
hours. Is there a significant difference between the average life
of all the manufacturer's batteries and the average battery life
of his sample?
α=5%.

A.) Identify null/alternative hypothesis

B.) Calculate the test statistic
C.) Find the critical value
D.) Illustrate the graph
 REVIEW
Hypothesis Testing
Two Types of Hypothesis Testing
Types of Errors
One-Tailed and Two-Tailed Test
Parameters
QUIZ
 QUIZ PART I:
PROBLEM SOLVING
(TOTAL 10 PTS)
 (A) State the null and
alternative hypothesis. (2 pts)

•A teacher finds the average score (B) Complete Solution.

on the second semester midterm Given (1 pts)
Formula (1 pts)
exam is 45. One of his students
Complete Solution (1 pts)
believes that this value is higher Final Answer (2 pts)
and decides to gather the scores of
30 of his classmates. He finds that (C) Illustrate the graph. (2 pts)

their average score is 47 with a (D) State the appropriate

standard deviation of 2.5. At a 99% conclusion. (1 pts)
confidence level, what is the
appropriate conclusion?
 QUIZ PART II:
TYPE I OR TYPE II
ERROR QUESTIONS
(TOTAL 10 PTS)
 THIS IS 5-ITEM MULTIPLE CHOICE PROBLEMS
ABOUT THE TWO TYPES OF HYPOTHESIS.
DIRECTIONS:
(1) READ THE QUESTIONS CAREFULLY.
(2) CHOOSE THE LETTER THAT CORRESPONDS
TO YOUR ANSWER.
(3) REVIEW YOUR ANSWERS BEFORE
SUBMITTING.
1. A quality control expert wants to test the null
hypothesis that an imported solar panel is an effective
source of energy. What would be the consequence of a
Type I error in this context?

A. They do not conclude that the solar panel is effective when it

is actually effective.
B. They conclude that the solar panel is effective when it is not
actually effective.
C. They conclude that the solar panel is effective when it is
actually effective.
D. They do not conclude that the solar panel is effective when it
is not actually effective.
2. A resort owner does a daily water quality test in their swimming
pool. If the level of contaminants is too high, then he temporarily
closes the pool to perform a water treatment. We can state the
hypotheses for his test as:
Ho: The water quality is acceptable.
Ha: The water quality is not acceptable.
What would be the consequence of a Type I error in this setting?

A.The owner closes the pool when it needs to be closed.

B. The owner closes the pool when it does not need to be closed.
C. The owner does not close the pool when it needs to be closed.
D. The owner does not close the pool when it does not need to be
closed
3. In terms of safety, which
error has more dangerous
consequences in this setting?
A. Type I
B. Type II
4. A quality control expert wants to test the null hypothesis
that an imported solar panel is an effective source of energy.
What would be the consequence of a Type II error in this
context?

A. They conclude that the solar panel is effective when it is

actually effective.
B. They do not conclude that the solar panel is effective when it
is actually effective.
C. They conclude that the solar panel is effective when it is not
actually effective.
D. They do not conclude that the solar panel is effective when it
is not actually effective.
5. A resort owner does a daily water quality test in their swimming
pool. If the level of contaminants is too high, then he temporarily
closes the pool to perform a water treatment. We can state the
hypotheses for his test as:
Ho: The water quality is acceptable.
Ha: The water quality is not acceptable.
What would be the consequence of a Type II error in this setting?

A. The owner does not close the pool when it does not need to
be closed.
B.The owner closes the pool when it needs to be closed.
C. The owner does not close the pool when it needs to be
closed.
D. The owner closes the pool when it does not need to be
closed.
 QUIZ PART III:
STATE THE
HYPOTHESIS
(TOTAL 10 PTS)
 STATE THE HYPOTHESIS
A 5-ITEM QUIZ OF STATING THE HYPOTHESIS (NULL
AND ALTERNATIVE HYPOTHESIS) OF EACH PROBLEM.

DIRECTIONS:
IN EACH NUMBER, A 2-POINTS PROBLEM IS GIVEN.
(1) READ IT CAREFULLY,
(2) STATE THE NULL HYPOTHESIS AND ALTERNATIVE
HYPOTHESIS WITH SOLUTION.
(3) REVIEW YOUR ANSWERS BEFORE SUBMITTING AND
HOPE FOR A HIGH SCORE!
EXAMPLE OF A SOLUTION:

𝐻0 : The mean score of the students

in their Statistics test is 55 or 𝜇 = 55.
𝐻𝑎: The mean score of the students in
their Statistics test is not 55 or 𝜇 ≠ 55.
1. Hare claims that their house and lot cost an
average selling price of Php800,000 in the
market. His brother wants to know whether
Hare's claim is accurate or not.

Let 𝜇 be the population mean selling price and x

be the mean selling price of the house and lot.
𝐻o :
𝐻𝑎:
2. Bleu believes that her group scored an
average of 90% on the peer-evaluation survey.
Haven, on the other hand, disagrees with this
and decides to conduct a survey.

Let 𝜇 be the population mean rate and x be the

mean rate of Bleu's group on the peer-evaluation
survey.
𝐻o :
𝐻𝑎:
3. A manufacturer of bottled water claims that
their 60-mL labeled bottle contains a mean of 58
mL of water. Wyndell wishes to test if the mean
amount of water in a 60-mL labeled bottle is less
than 58 mL.
Let 𝜇 be the population mean volume of water in a
labeled bottle and x be the mean volume of water
produced by the manufacturer on a 60 mL labeled bottle.
𝐻o :
𝐻𝑎:
4. Louzelle believes that their daily supply of
tissue in their company is an average of 400
boxes. Krelian believes that it is too much and
tests it to prove that it is less than 400 boxes.
Let 𝜇 be the population mean daily supply of tissue
boxes and x be the mean daily supply of tissue boxes
in their company.
𝐻o :
𝐻𝑎:
5. Martin claims that he only drinks an average of
1.5 oz of vodka a week. His wife, Temia, doubts it
and decides to put it into a test to know if her
husband drinks more than 1.5 oz of vodka a week.

Let 𝜇 be the population mean vodka intake in a

week and x be the mean of Martin's vodka intake
in a week.
𝐻o :
𝐻𝑎:
ANSWER KEY I
A.)
𝐻o : The average score of the students in
the second semester midterm exam is 45,
𝜇 = 45
𝐻𝑎: The average score of the students in
the second semester midterm exam is
greater than 45, 𝜇 > 45
B.) Given: Formula:
X̄ = 47 t-test formula
µ = 45 t = X̄ - µ
n = 30 σ
σ = 2.5 √n
Solution:
t = 47 - 45 2
2.5 = 2.5 = (2/1)(√30/2.5) = 4.3818
√30 √30
C.)
D.)
The t-crit value is less than the
value of the t-computed value,
therefore the null hypothesis is
rejected and the alternative
hypothesis is accepted.
ANSWER KEY II

1. A 2. B 3. B
4. C 5. C
ANSWER KEY III
1. 𝐻o : The mean selling price of the house and lot is
Php800,000 or 𝜇 = Php800,000.
𝐻𝑎: The mean selling price of the house and lot is
NOT Php800,000 or 𝜇 ≠ Php800,000.

2. 𝐻o : The mean rate of Bleu's group is 90% or 𝜇 =

90%.
𝐻𝑎: The mean rate of Bleu's group is NOT 90% or 𝜇
≠ 90%.
3. 𝐻o : The mean volume of water in a 60 mL
labeled bottle is 58 mL or 𝜇 = 58 mL.
𝐻𝑎: The mean volume of water in a 60 mL labeled
bottle is less than 58 mL or 𝜇 < 58 mL.

4. 𝐻o : The mean daily supply of tissue boxes is

400 boxes or 𝜇 = 400 boxes.
𝐻𝑎: The mean daily supply of tissue boxes is less
than 400 boxes or 𝜇 < 400 boxes.
5. 𝐻o : The mean of Martin's vodka intake
in a week is 1.5 oz or 𝜇 = 1.5 ounces.
𝐻𝑎: The mean of Martin's vodka intake in
a week is 1.5 oz or 𝜇 > 1.5 ounces.
THANK YOU
VERY MUCH!