COLLEGE OF ACCOUNTANCY

C-AE9 STATISTICAL ANALYSIS WITH SOFTWARE APPLICATIONS

First Semester | AY 2024-2024

Lesson 8: HYPOTHESIS TESTING

PARAMETRIC TESTS
USING CRITICAL VALUE METHOD
Time Frame: Week 9 (3 hours)

1. Overview
This CAE9 Lesson 8 that is good for 3 hours (equivalent to 3 meetings or
1 week of class sessions), is aimed at three things: (1) to illustrate the process of testing
hypothesis using parametric tests by critical value method (2)to solve problems
applying t-test(one-sample) (3) To perform activities associated with the lessons
presented.

2. Desired Learning Outcomes

After the three -hour home-based study period, you are expected to have:
(1) Read exhaustively lessons 8.1 and 8.2;
(2) Explained the process of testing hypothesis using parametric tests and how it
differs from nonparametric tests.
(3) Described the requirements for choosing one-sample t-test.
(4) Solve problems concerning t-test for one sample using critical value method.
(5) Accomplished the activities related to the lessons presented in the Progress
section of the module.
(6) Carried out the evaluation part of the module.
3. Content
Lesson 8.1 Topics: Testing Hypothesis Using Critical
Value Method; Parametric Tests
In Lesson 7, we started off with a major topic of inferential statistics as we use sample
statistics to test hypotheses made about population parameters. Before proceeding to the
actual problem solving on parametric tests using the critical value method, recall what
parametric test is and how it differs with nonparametric tests.
Definition of Parametric Test
• The parametric test is the hypothesis test which provides generalizations for making
statements about the mean of the parent population. A t-test based on Student’s t-statistic,
which is often used in this regard.
• The t-statistic rests on the underlying assumption that there is the normal distribution of
variable and the mean in known or assumed to be known. The population variance is
calculated for the sample. It is assumed that the variables of interest, in the population are
measured on an interval scale.
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FACULTY: GRACE C.SADAC PhD 1 | Page

 COLLEGE OF ACCOUNTANCY
C-AE9 STATISTICAL ANALYSIS WITH SOFTWARE APPLICATIONS
First Semester | AY 2024-2024

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PARAMETRIC TESTS

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Test Concerning Means
A. Test for one sample mean
a. When σ is known, use z-test

b. When σ unknown, use t-test

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 COLLEGE OF ACCOUNTANCY
C-AE9 STATISTICAL ANALYSIS WITH SOFTWARE APPLICATIONS
First Semester | AY 2024-2024

Where σ is the standard deviation

For a z-test:
 The sample is large (n>30), so the central limit theorem applies and we can use the
normal distribution.
 When applying the central limit theorem, we can use the sample standard
deviation s as an estimate of the population standard deviation σ whenever σ is
unknown and the sample size is large (n>30).
For a t-test:
 T-test is used for claims about µ when n ≤ 30 and σ is unknown.
 If the population is essentially normal, then the t-distribution is essentially a
Student t-distribution for all samples of size n. ( The Student t distribution is often
referred to as the t distribution).

Lesson 8.2 Topics: Hypothesis Testing using T-test One-

Sample; Problem Solving Using T-Test One Sample

Sample Problems: T-Test One Sample

Example 1.
A random sample of 20 drinks from a soft-drink machine has an average
content of 21.9 deciliters, with a standard deviation of 1.42 deciliters. At .05 level of
significance, test the hypothesis that μ = 22.2 deciliters against the alternative that μ <
22.2 and assume that the distribution of the soft drinks contents be normal.
Solution:
a) Null Hypothesis H0 : μ = 22.2 deciliters
b) Alternative Hypothesis Ha : μ < 22.2 deciliters
c) How to determine the Critical Value
Use the following data to locate the critical value from the t-Table.
 Level of Significance α = 0.05,

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 COLLEGE OF ACCOUNTANCY
C-AE9 STATISTICAL ANALYSIS WITH SOFTWARE APPLICATIONS
First Semester | AY 2024-2024

 One-tailed test, left directional

 degrees of freedom (df) = n-1=20-1=19 (for one-sample t-test the degrees of
Freedom = n-1)
Therefore, the Critical value = -1.729;
d) Criterion: Reject the null hypothesis if computed t < -1.729 and otherwise, accept it.
e) Test Statistics:
Note: The student’s t statistic can be used since our sample size n = 20 is
small and the soft drinks content was assumed to be normally distributed.
x  
t 
s
n
Compute:
21.9  22.2
tc   0.945
1.42
20

f) Decision: Since computed t = -0.945 is greater than -1.729, null cannot be rejected
g) Conclusion: The mean content of the soft drinks is equal to 22.2 deciliters. In
other words, though there is a numerical difference of 0.3, this difference can be
attributed to chance.

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 COLLEGE OF ACCOUNTANCY
C-AE9 STATISTICAL ANALYSIS WITH SOFTWARE APPLICATIONS
First Semester | AY 2024-2024

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 COLLEGE OF ACCOUNTANCY
C-AE9 STATISTICAL ANALYSIS WITH SOFTWARE APPLICATIONS
First Semester | AY 2024-2024

References:
Amora, Johhny (2014). Statistical Data Analysis Using SPSS (Modules 1-5). Taft Ave.Manila.
Devoke, Jay L.(2005). Statistics. Pacific Gorve, California.
Frankfurt, N. & Leon-Guerrero, A. (2006). Social Statistics for a Diverse Society. Thousand
Oaks, CA Pine Forge Press.
Gonzales, J & Noncom, R. (2015). Essential Statistics. Diliman Quezon City. Philippines. Phil
Maxcor Publishing House, Inc.
Kremelberg, David (2011). Practical Statistics.SAGE Publication.Los Angeles
Lind, Douglas A., Marchal, William G. & Wathen, Samuel A. (2010). Statistical Techniques in
Business and Economics. McGraw –Hill Irwin. New York, NY.
Parreno, Elizabeth B.(2006).Introduction to Statistics. C&E Publishing Inc. Quezon City.
Rosner, B. (2012). Biostatistics. Singapore Cengage Asia Pte Ltd.
Spat, Chris (2008).Basic Statistics. Wadsworth, Australia.

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