Defining Hypothesis Testing
Defining Hypothesis Testing
Defining Hypothesis Testing
Submitted
In Partial Fulfillment
By:
Alex, Ezikiel
Alpino, Harvey
Amio, Willliam
Calingo, Miguel
Gania, Joshua
January 2020
Hypothesis Testing
the nature of the data used and basis of analyzation. It is mainly used to assess the
To the students. This study would give students the knowledge about
hypothesis testing with its process and formulas that could be applied to statistical
To the teachers and instructors. This study would give the teachers with views
This study is limited to aimed to be done inside Holy Angel University only and
will tackle the concepts, processes holy angel university having financial difficulties, and
engineering students, where their names, year level and section are made confidential.
A research is a systematic work that aims to find out or uncover certain information or more
specifically, answers to the questions that researchers have asked or wondered even before
they have started the project in the first place. Researches are generally daunting and are done
over a very long period of time, which can range from a few weeks to a few months and
sometimes even years. This is due to the fact that a research has several parts that make up its
priority. The precision of data and its accuracy will determine the course of the research and
Hypothesis Testing
Hypothesis testing is the action or act in statistical researches where the researcher, or
in this case, the analyst tries to analyze the initial hypotheses or claim in regards to a
hypothesis. Simply put, hypothesis testing is the part of a research where statistics is used to
take a look at the given data or analyze it. This part of the research must be taken into account
at a very early part of your research planning since there may be a possibility that some of the
data that has been collected may not be clearly analyzed or are too obscure to categorize or
label and thus, will not be fully able to complement the hypothesis test. It would be more
convenient too if the choices were limited and not fully open as well.
Basic Steps of Hypothesis Testing
According to Majaski (2020), all hypotheses are tested using a four-step process:
1. The first step is for the analyst to state the two hypotheses so that only one can
be right.
2. The next step is to formulate an analysis plan, which outlines how the data will be
evaluated.
3. The third step is to carry out the plan and physically analyze the sample data.
4. The fourth and final step is to analyze the results and either reject the null
hypothesis, or state that the null hypothesis is plausible, given the data.
When testing the given hypotheses, it is important to look at the hypotheses first and
foremost or make a claim if there are still none. Two preferably, one that signifies no changes or
difference, and one that signifies that there is a difference. The first hypothesis will be dubbed
the Null Hypothesis which is denoted by H0, it is the prediction or statement that claims that
there are no significant difference or relation between the data; this is the hypothesis that is
expected to be rejected. The null hypothesis should be stated because it is the primary
hypothesis that will be tested. A study should not be designed in such a way that it will
mistakeably support the null hypothesis. The null hypothesis being rejected, is what the design
Ha. It is the expected result findings of the study. This is also the point where the research will
establish the tail or the direction that it leans on. Alternative hypotheses can be classified into
one of the following two, they can be two tailed, or one tailed. In the case of the one tailed, it
can be separated further into whether it is only limited to being either lower or higher, but never
both. If it is lower than a certain amount, then it will be a left tailed test, if higher, then a right
tailed test. In two tailed tests it can go either way. There exists an Experimental Hypothesis as
well, when it comes to experimental research. These two are commonly mistaken for one
another. They are similar in the fact that they are used for predicting the changes between
groups. All experimental hypotheses are alternative, but not all alternative hypotheses can be
classified as experimental.
Examples:
-The proportion of detergent users who prefer Brand A is higher than 50%
Before the test can proceed, it should be noted that sometimes there are instances
where errors may occur. The two kinds of errors are given below.
In the event that the null hypothesis was found to be true, and it was accepted then no errors
are committed. If for whatever reason, it was rejected then a Type I error was committed. In the
event that the null hypothesis was found to be false and was accepted, then a Type II error
was committed.
Following the statements of the hypotheses, the test continues with the collection of data, from
the given, namely the mean scores and anything that will be used in the test statistic.
Test Statistic
The test statistics are a way to compare the results that were conceived with the regular
population. A test statistic can be computed in three different ways and will depend on the
situation or what results is being aimed for. The test statistic will be solved using a Z-test if the
comparison of a population mean to a sample is the aim. T-test will be used if the hypotheses
will be tested and if determining the difference between two independent sample groups is the
goal. T tests are best used for when the sample size is less than 30, and Z tests are used when
the sample size is larger than 30. There are other types of tests as well aside from these such
as the Chi Square which is used for an association between two categorical variables relating
to the population sample. There is also the Homogeneity of Variance which is used to test the
likeness or similarity of dispersion parameters when two or more population samples are given.
Analysis of Variance however, focuses on the differences between means in at least more
than two groups. Mood’s Median compares the medians of at least 2 population samples.
In the case of Welch Test however, it is similar to the Mood’s Median except this time it
compares the equality of means between two samples. Kruskal-Wallis H Test compares two
or more groups with a variable which should not be dependent, based on a dependent variable.
The Box Cox Power Transformation transforms a data set into a normal distribution
When determining if the null hypotheses will be rejected, a threshold must first be established.
This threshold is known as the Critical Value. The critical value’s range depends on the type of
test it will be as well as the confidence level. Generally, 95% is the most commonly used or
90%, these percentages will roughly translate to 0.1 or 0.05. Just like with the test statistic, the
The table below can be referred to for the common confidence levels:
0.90 +/-1.645
0.91 +/-1.70
0.92 +/-1.75
0.93 +/-1.81
0.94 +/-1.88
0.95 +/-1.96
0.97 +/-2.17
0.98 +/-2.33
0.99 +/-2.575
Step 1: Subtract the confidence level from 100% (1)
This is the part where a conclusion will be drawn from the results of the test. The
test statistic will determine if the null hypothesis is rejected or accepted. The critical
values will play the roles of the thresholds when deciding whether to accept or reject the
hypothesis.
EXAMPLES
TWO TAILED
Problem 1
A new sneakerstore (Sneakers_PH) claims that his fees are lower than that of
your current sneakerstore (Pumped-up Kicks). Data available from an
independent research firm indicates that the mean and standard deviation of all
Pumped-up Kicks clients are $18 and $6, respectively. A sample of 100 clients of
Pumped-up Kicks is taken and fees are calculated with the new rates of
Sneakers_PH. If the mean of the sample is $18.75 and the sample standard
deviation is $6, can any inference be made about the difference in the average
bill between Pumped-up Kicks and Sneakers_PH store?
Solution:
(18.75−18)
Z= =1.25
6
( )
√ 100
This calculated Z value falls between the two limits defined by: -
Z2.5 = -1.96 and Z2.5 = 1.96.
This concludes that there is insufficient evidence to infer that there is
any difference between the rates of your existing broker and the new
broker. Alternatively, the p-value = P(Z< -1.25)+P(Z >1.25) = 2 *
0.1056 = 0.2112 = 21.12%, which is greater than 0.05 or 5%, leads
to the same conclusion.
Problem 2
Solution:
( P 1− p 2)
Z=
√ P(1−P)
√ 1
+
1
n1 n2
N1= 200
N2 = 200
64 92
P1= =0.32 P2 = =0.46
200 200
x 1+ x 2 64+ 92
P= = =0.39
n 1+n 2 200+200
(0.32−0.46)
Z= =2.869
√ 0.39( 1−0.39)
√ 1
+
1
200 200
This calculated Z value falls outside the two limits defined by: - Z2.5 =
-1.96 and Z2.5 = 1.96.
ONE TAILED
Problem 1
An alternator manufacturer must produce its alternators so that they are 95% confident
that it runs at less than 71.1° C under stress test in order to meet the production
requirements for sale to the US government. The stress test is performed on random
samples drawn from the production line on a daily basis. Today’s sample of 7
alternators has a mean of 71.3° C and a standard deviation of 0.214° . Is there a
production quality issue?
Solution:
Ý −μ 71.3−71.1
t c= = =2.47
s / √ n 0.214/ √ 7
Since t c is clearly in the “Reject” region, then we must reject the null
hypothesis. The null hypothesis was “H0: The population mean is less than
or equal to 71.1° C”. Rejecting that means that the sample was NOT
within the bounds of what we would find acceptable if the population mean
were truly at 71.1° C.
Problem 2
A sociologist has predicted that in a given city, the level of absenteeism in the
upcoming elections will be a minimum of 40%. Of a random sample of 200 individuals
from the voting population, 75 state they will likely vote. Determine with a significance
level of 1%, if the hypothesis can be accepted.
Solution:
This conclude that the null hypothesis, H0, should be accepted as it can be stated with a
confidence level of 1% that absenteeism will be at least 40% for the upcoming election.
Problem 3
An up and coming new computer manufacturer sets the retail cost of their new
computers based in the manufacturing cost, which is $1800. However, the
company thinks there are hidden costs and that the average cost to manufacture
the computers is actually much more. The company randomly selects 40
computers from its facilities and finds that the mean cost to produce a computer
is $1950 with a standard deviation of $500. Run a hypothesis test to see if this
thought is true.
Solution:
(1950−1800)
Z= =1.897
500
( )
√ 40
This calculated Z value falls greater than Z0.05 = 1.65, which is 1.897
This concludes that the up and coming computer manufacturer does
not have to worry about any hidden costs and that the average of
manufacturing a computer is much less.
Problem 4
A researcher believe that the average return on all Filipino stocks was greater
than 2%. In this case, the researcher is making a statement about. The
population mean (u) of all Filipino stocks. The sample mean of 36 observations of
Filipino Stocks is 4 and the standard deviation of the Population is 4.
Solution:
Rejection region: Using the Z- table and 5% level of significance, the critical
value is Z0.05 = 1.65
( 4−2)
¿ =3
4
( )
√ 36
This calculated Z value falls greater than Z0.05 = 1.65, which is 3
In conclusion because the test statistic z = 3 is greater than the
critical value of 1.645, we reject the null hypothesis in favor of the
alternative hypothesis that the average return on all Filipino stocks is
greater than 2%.
Research Design
This study is a definitive study. It is a phenomenology design that does not meet
definitive study attempts to create a design scheme which defines and conceptualizes
Hypothesis Testing.
Research Locale
The university is open for the students of preschool, elementary school, junior high
school, senior high school, and college. It is known to the whole central Luzon region as
a university that molds students to hone their skills for competence and to cope with the
Bibliography
Majaski C. (2020, January 27) Hypothesis Testing. Retrieved from https://www.
investopedia.com/terms/h/hypothesistesting.asp