INFERENTIAL STATISTICS
HYPOTHESIS TESTING
DEFINITION of TERMS
STATISTICAL HYPOTHESIS is an assumption or an
educated guess about the population parameter.
TWO–TAILED TEST
It is a test when the regions of rejection is located on
both ends of the distribution
It uses the ≠ symbol
is a guess or prediction made by the researcher
regarding the possible outcome of the study
What is HYPOTHESIS TESTING ?
It is the process of making inference or generalization
on population parameters based on the results of the
study on samples
It is deciding between what is reality and what is
coincidence
NULL HYPOTHESIS is the starting point of the testing
process, thus, it serves as the working hypothesis
It is known as a no difference or a no relationship
hypothesis
It always contains the equal “=” sign
ALTERNATIVE HYPOTHESIS It generally represents the
idea which the researcher wants to prove
It specifies an existence of a difference or a
relationship and it also specifies that one group is
better than the other
It is a directional hypothesis because uses the <, > or ≠
symbols
TYPES of ERRORS
TYPE I ERROR is the error committed when the Ho is
rejected when it is true and it is also known as the
ALPHA () ERROR
TYPE II ERROR is the error committed if the Ho is
accepted when it is false and it is also known as the
BETA () ERROR
LEVEL of SIGNIFICANCE is the probability of
committing a TYPE I ERROR
LEVEL of SIGNIFICANCE is the probability of
committing a TYPE I ERROR
KINDS of TEST
Ho: The average height of Filipino women is 5 feet.
( = 5 feet)
ONE–TAILED TEST
Ha: The average height of Filipino women is greater
than 5 feet. ( > 5 feet) (one-tailed test)
It is a test when the region of rejection is located at
only one extreme of the range of values for the test
statistics.
Ha: The average height of Filipino women is less than
5 feet. ( < 5 feet) (One-tailed test)
It is either left direction or right direction.
Ha: The average height of Filipino women is not 5
feet. (  5 feet) (Two-tailed test)
It uses the < or > symbols
Ho: The average height of Filipino women is 5 feet. (
= 5 feet)
Ha: The average height of Filipino women is greater
than 5 feet. ( > 5 feet) (one-tailed test)
STEPS in TESTING a HYPOTHESIS
1. Formulate the Ho and state also the Ha.
2. Determine the appropriate level of
significance to be used.
3. Choose an appropriate test statistic and
determine the kind of test to be used.
4. Determine the critical value or tabular value
of the test statistic.
5. Compute or find the value of the test statistic
using the sample data.
6. Make the decision/conclusion.
Make the decision/conclusion.
ACCEPT Ho if the computed value is less than the
critical or tabular value.
REJECT Ho and ACCEPT Ha if the computed value is
greater than the critical or tabular value.
EXERCISE: State the Ho and the Ha that would be
used for a hypothesis test related to each of the
following statements:
1. Is the average weight loss of people enrolled in an
aerobics class for one month 8.6 pounds?
Ha: Male students of Isabela State University-Ilagan
are heavier than the female students. (X1 > X2) Onetailed test.
4. Is there a significant relationship between the
prelim grades and the midterm grades of 10 students
in Mathematics?
Ho: There is no significant relationship between the
prelim grade and the midterm grades of 10 students
in Mathematics.
Ha: There is a significant relationship between the
prelim grade and the midterm grades of 10 students
in Mathematics.
TESTING THE SIGNIFICANCE of DIFFERENCE BETWEEN
SAMPLE MEAN & POPULATION MEAN
A. z–TEST the statistical test being used when the
population standard deviation is known and when n
> 30.
B. t–TEST is the statistical being used when the given
is the sample standard deviation and when n < 30.
Z-TEST
This type of test or statistical tool is used when the
given is the population standard deviation.
ONE TAILED TEST
It is a kind of test where the symbol used is either < or
> symbol and it has only one region of rejection.
≠ symbol
Ho: The average weight loss of people enrolled in an
aerobics class for one month is 8.6 lbs.
This is the symbol used when the regions of rejection
are located on both sides of the distribution
(X = 8.6 lbs.)
NULL HYPOTHESIS
Ha: The average weight loss of people enrolled in an
aerobics class for one month is not 8.6 lbs.
Given the statement: “There is no significant
difference in the Academic performance of the male
and female students of ISUI”. What type of hypothesis
is the given?
(X ≠ 8.6 lbs.) Two-Tailed Test
2. Is there a significant difference between the
academic performances of male and female students
of BSE?
Ho: There is no significant difference between the
academic performances of male and female students
of BSE. (1 = 2)
Ha: There is a significant difference between the
academic performances of male and female students
of BSE. (1 ≠ 2)
3. Are male students of Isabela State UniversityIlagan heavier than the female students?
Ho: Male students of Isabela State University-Ilagan
are as heavy as the female students. (X1 = X2)
DIFFERENCE BETWEEN TWO SAMPLE MEANS
INDEPENDENT SAMPLES
The two sample means are taken from two different
groups
DEPENDENT SAMPLES
This also known as Paired Observation.
The two sample means are taken from the same or
one group