Chapter I
INTRODUCTION
Background of the Study
Philippines is an agricultural and tropical country producing a
variety of vegetation. Small communities even those located in the city
practice organic farming to save more, ensure quality and inexpensive
produce. Organic farming is a method of livestock and crop production
without the use of fertilizers, pesticides, growth hormones, antibiotics
and genetically modified organisms. But this still does not ensure the
same quality of produce and there are many factors to consider that may
affect the growth of the plant (Far Eastern Agriculture, 2012).
Pondus Hydrogenii or more commonly known as pH indicates a
solution’s acidity or alkalinity. Acidity is essential for life forms on earth
as it often determines the characteristics, quality, absorbability and
solubility of different substances. With the correct acidity, enzymes
function to control biological processes in organisms. A demonstration of
the importance of pH is that a small fluctuation in the blood’s acidity can
be jeopardizing (Fondriest Environmental, 2013).
Varieties of plants have different tolerance for pH levels. Some may
flourish in mildly acidic, neutral, or alkaline environments. Water is
another factor that affects the pH level of the environment of the plant.
Abelmoschus esculentus (okra plant) is a vegetable known for its high
dietary fiber content. Usually consumed by diabetics, and has many
more benefits. It grows best on loamy soil, needs full exposure to sun,
therefore, height is an important factor, and its peak season is at
summer time. This research study aims to see the effect of different pH
levels of water to the growth of an Abelmoschus esculentus (okra plant)
1
and to determine which pH level is best to achieve optimum plant height
(Tong, 2016).
Statement of the Problem
This study primarily aims to help contribute information about
the effect of different pH levels of water (1.0, 4.0, 7.0, 10.5, and 14.0) to
the growth of Abelmoschus esculentus (okra plant) and determine which
pH level is best for the growth of the A. esculentus.
Specifically, it aims to answer the following questions:
1. How do different pH levels of water affect the height of A.
esculentus?
2. Which pH level of water is best to achieve optimum plant height
of A. esculentus?
Initial hypotheses are the following:
1. There will be no significant difference on the effect of different
pH levels on the height of the plant.
2. Acidic pH levels produce optimum plant height.
Alternative hypotheses:
1. Different pH levels will have a significant effect on the height
of the plant.
2. Basic pH levels produce optimum plant height.
2
Significance of the Study
The researcher’s purpose for conducting this study is to find out if
pH level of water affects the growth of an Abelmoschus esculentus (okra
plant) and which pH level of water is best to achieve optimum height.
The community may receive benefits from this research study especially
households or communities that practice organic farming. Further
research may be conducted to validate of the effect of pH levels of water
to the growth of an A. esculentus (okra plant) and different ways to raise
or lower the pH level of the environment fit for the pH preference of the
plant.
Scope and Delimitations
The focus of the study is the effect of different pH levels of water to
the growth, specifically the height of Abelmoschus esculentus (okra plant)
and determine which pH level produces optimum plant height. It used
water with pH levels ranging from 1.0, 4.0, 7.0, 10.5, and 14.0.
Calamansi juice (citric acid) and baking soda may be used as substitute
for sulphur and agricultural lime respectively to raise or lower the pH
level of water. It does not include other tests of other pH levels of water,
tests on other types of plant, and different amounts of water, besides the
one used in the experiment. This study only used pH meter to determine
the pH level of water, soil pH tester for the pH of soil, method of
measuring height via ruler. This study was conducted for 14 days
including data collection.
3
Definition of Terms
Abelmoschus esculentus - scientific name of the cultigens vegetable plant
okra or okro or in English – speaking countries ochro or ladies’ fingers. It
is a flowering plant in the mallow family. It is valued for its edible green
seed pods.
Acidity - the amount or level of acid present in substances such as water,
soil or wine. Acidity often determines the characteristics, quality,
absorbability and solubility of many substances.
Agricultural lime - a soil additive made from pulverized limestone or
chalk, which has the primary active component of calcium carbonate
used to increase alkalinity of soil. It is also called aglime, agricultural
limestone, garden lime or liming.
Alkalinity - the quantitative capacity of an aqueous solution to neutralize
an acid. This usually measures the basicity or how “strong” the bases are
in a solution
Cultigen - a plant that has been altered by humans through a process of
selective breeding.
pondus Hydrogenii - the indicator of acidity or alkalinity of a particular
solution. The pH value usually varies between 0 and 14. A solution with
a pH value ranging from 0 to 7 is considered an acid and a value in
between 7 to 14 is alkaline. A pH value of 7 is considered neutral.
4
Sulphur - a pale yellow, odorless, brittle solid, which is insoluble in water
but soluble in carbon disulphide. Sulphur is essential to life. It is a
minor constituent of fats, body fluids, and skeletal minerals. This is can
also come in powdered forms usually used in agriculture to lower pH
levels of soil.
5
Chapter II
REVIEW OF RELATED LITERATURE
Abelmoschus esculentus (okra plant)
Okra, also known as “lady’s fingers” and “gumbo,” is a green
flowering plant that belongs to the same family as hibiscus and cotton.
The term “okra” commonly refers to its edible seedpods. It contains
potassium, vitamin B, vitamin C, folic acid, and calcium, it also has low
calories and has high dietary fiber content. Okra has been suggested to
help lower cholesterol and manage blood sugar in cases of type 1, type 2,
and gestational diabetes (Watson, K., 2016).
According to P.S. Tong (2016), the okra plant has been cultivated
for nearly centuries originating from Africa and now widely cultivated in
tropical or sub-tropical countries. There are numerous uses for this plant
such as: source of food pertaining to the vegetable itself and its flower
buds; using its mucilage to different dishes, clarifying sugar cane juice in
making molasses, and glazing paper in China, okra leaves can also be
used as cattle feed, roasted okra seeds as substitute for coffee and it can
also be used to extract edible oil; its seeds, fruits, mucilage and roots are
used in some medical practices and lastly, its stem yields an inferior fiber
that can be used in creating cord and paper.
Okra prefers well-drained, sandy soils that are high in organic
matter, but it can be grown in a wide variety of soils. Okra can tolerate a
pH range of soil from 5.8 to 6.8 and grows best in full sunlit area. It is
recommended to plant when soils have warmed up to at least 65 degrees
F at a 4-inch depth (Westerfield, R., 2014).
6
pH level
The pH (pondus Hydrogenii) indicates a solution’s acidity or
alkalinity. A solution with a pH value of 0 to 7 is acid and one of 7 to 14
is alkaline. A pH value of 7 is considered neutral. The pH of tap water is
generally a little higher due to the presence of calcium. Acidity often
determines the characteristics, quality, absorbability and solubility of
many substances. This is how enzymes, which are responsible for almost
all biological processes in organisms, work, but only with the correct
acidity (Fondriest Environmental, 2013).
One of the most important factors determining the pH value in a
solution or in the substrate is the buffering capacity. The buffering
capacity in this instance means that there is a balance present that
continually restores itself. The buffering capacity and the substrate’s
acidity depend on its composition and freshness. The presence of organic
material, calcium and bicarbonate generally determine the pH. Clay
always contains calcium carbonate and has a relatively high pH value
which is difficult to change, while peat and sandy soils are acid
(Fondriest Environmental, 2013).
The plant itself has great influence on the acidity. The roots will
secrete either acid or alkaline substances depending on the crop’s stage
of development, the food available, the differences in root temperature
and light intensity. So the pH of the root environment constantly
fluctuates. A sophisticated feeding balance during the different phases of
development will keep the pH in the root environment within acceptable
limits (Tiamson, et. al, 2015).
When cultivating in substrate pH values of between 5.0 and 6.4
are generally fine for the root environment depending on the plant. There
will not be any adverse effects if the values are a little higher or lower.
Immediate adverse effects will only be seen with values lower than 4 and
7
higher than 8. pH values lower than 4 often cause immediate damage to
the roots. In addition, heavy metals, including manganese and iron are
absorbed so well that they can poison the plant (necrosis). Values
between 7 and 8 are not immediately harmful for the plant. Nutrients
such as iron, phosphate, and manganese are less available then which
will lead to deficiencies such aschlorosis and developmental problems in
the long run (pH acidity, n.d.).
8
Chapter III
RESEARCH METHODOLOGY
Research Design
The study utilized the Randomized Complete Block Design (RCBD)
(See Appendix B) because only one (1) independent variable was
manipulated in the study: the pH level of water 1.0, 4.0, 7.0, 10.5, and
14.0 respectively. The variables that remained constant throughout the
study were the following: the amount and pH level of soil used, amount
of water, growth time, calamansi juice (citric acid) as substitute to
sulphur to lower pH, baking soda as substitute to agricultural lime to
raise pH, plastic cups used as pots, measuring method via ruler, location
of testing, process for testing soil pH via soil pH tester and the process of
testing through pH meter.
Preparation of the Set-up
Twenty (20) A. esculentus seeds were soaked in 30 ml of tap water
for 12 hours in a bowl. There were 5 set-ups namely set up A for water
with pH level of 1.0, set up B for water with pH level of 4.0, set up C for
water with pH level of 7.0, set up D for water with pH level of 10.5, set up
E for water with pH level of 14.0. Each set up was placed in a plastic cup
with their respective labels. Each cup was filled with 150 grams of soil of
the same pH level then 4 seeds were sown per set-up. Each set-up was
repeated twice to conduct 3 trials.
125 ml or ½ cup of tap water was prepared per set up. The pH
level was tested and adjusted with baking soda or calamansi juice
accordingly per set up. Each set-up was watered 20ml once with their
respective assigned pH levels daily.
9
The set-up was divided into 5 groups: set-up A, B, C, D and E
respectively. Each group had three (3) cups to represent trials 1, 2 and 3.
The cups in each set-up was labeled accordingly: A1, A2, A3 for water
with pH level of 1.0, B1, B2, B3 for water with pH level of 4.0, C1, C2, C3
for water with pH level of 7.0, D1, D2, D3 for water with pH level of 10.5,
and E1, E2, E3 for water with pH level of 14.0. Set-up C will be the
control group while set-ups A, B, D and E will be the experimental group.
Data Collection
Daily height of each plant was measured and recorded in a span of
14 days. Collected data from each set-up was presented in a data table
and the average measures of height (mean) of the plants were calculated.
Average plant height was presented in a graph and average daily height
was shown in a time-series graph.
Analysis
For the analysis of the data, this study used the F-test and the
Tukey test as the statistical tool to see if there is any significant
difference between the mean heights of plants in each set-up. The data
was compared and the tallest average plant height and shortest plant
height were determined. The pH levels from shortest to tallest plant
height produced was then ranked. For each set-up the tallest and
shortest plant height achieved in each level was identified. Lastly, the
research question and hypotheses was addressed then the conclusion
and results were formulated and discussed respectively.
10
Chapter IV
RESULTS AND DISCUSSION
The effect of different water pH levels in the growth of A. esculentus
was investigated, focusing on the height of the plant. The height of each
plant in the different set-ups was measured and recorded after 14 days
of exposure to the water samples. The average daily height of the plants
in each set-up is shown in Table 1.1
Table 1.1 The Effect of Different pH levels on the Average Daily Height
(cm) of A. esculentus
SET-UP
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
DAY 6
DAY 7
DAY 8
DAY 9
DAY 10
DAY 11
DAY 12
DAY 13
DAY 14
A - 1.0
B - 4.0
C - 7.0
D - 10.5
E - 14.0
0
0.77
1.8
2.97
4.23
5.63
6.13
6
6.67
6.67
6.9
7.17
7.17
7.17
0
0.5
1.83
3.67
5.16
6.67
7.5
8
8.5
8.5
8.83
9.17
9.67
10.33
0
0.17
0.67
1.5
2.67
4.5
5.67
7.8
8.33
8.5
9.1
9.83
10
10
0
0.93
1.73
3.83
4.17
5.17
5.5
3.17
3.17
0
0
0
0
0
0
0
0
0.17
0.33
0.33
0.33
0
0
0
0
0
0
0
The data shows the averaged growth rate of the plants of trials 1, 2
and 3 of each set-up in a span of 14 days. Set-ups A, B and C grew
progressively each day while set-ups D and E yielded plants but then
withered on the 9th and 7th day respectively. According to the data
gathered Set-up B with the pH level of 4.0 achieved the tallest average
height of 10.33 cm; 0.33 cm higher than set-up C, the controlled group,
11
and 3.16 cm than set-up A. Ranked second is Set-up C with 10 cm, Setup A with 7.17 cm, and ranked last with the shortest average height is
Set-up D and E with 0 cm.
Figure 1.1 Average Daily Height (cm) of A. esculentus for 14 days
The data does not seem to support the first initial hypothesis
stating that there will be no significant difference on the effect of different
pH levels on the height of the plant but supports the second hypotheses
which states that acidic pH levels would produce optimum plant height.
Table 1.2. Height of each set-up per trial on final day (day 14)
DAY
TRIAL
1
14
2
SET-UP A
(1.0)
0 cm
Wilted
11.5 cm
Damaged
leaves
10 cm
SET-UP B
(4.0)
SET-UP C
(7.0)
5.5 cm
10.5 cm
13.5 cm
10.5 cm
12 cm
9.5 cm
3
SET-UP D
(10.5)
0 cm
Wilted
0 cm
Wilted
0 cm
Wilted
SET-UP E
(14.0)
0 cm
Wilted
Wilted Sprout
no established
roots
Wilted Sprout
no established
roots
The best pH level to achieve optimum plant height would be Setup B with a 4.0 pH level achieving the tallest height 13.5 cm on Table 2,
trial 2 and with the average height of 10.33 cm in Table 1. Though Set12
up A has the second tallest height of 11.5 cm, Set-up C is recommended
as all plants in the trials are healthy and achieved an average height of
10 cm while Set-up A trial 2 yielded damaged leaves and Set-up A trial 1
wilted.
Figure 1.2. Height of each set-up per trial on final day (day 14)
The data shows that on day 14, Trial 2 of set-up B yielded the
tallest plant height among the other trials of other set-ups. Trials 2 of
set-ups A, B and C produced the tallest plant height each in their own
respective set-up.
Detailed Computations on Appendix C
SET-UP A
(1.0)
0 cm
11.5 cm
10 cm
SET-UP B
(4.0)
5.5 cm
13.5 cm
12 cm
SET-UP C
(7.0)
10.5 cm
10.5 cm
9.5 cm
SET-UP D
(10.5)
0 cm
0 cm
0 cm
SET-UP E
(14.0
0 cm
0 cm
0 cm
𝑁𝐴 = 3
̅ 𝐴 = 7.17
𝑋
𝑆2 𝐴
= 39.083
𝑁𝐵 = 3
̅ 𝐵 = 10.33
𝑋
𝑁𝐶 = 3
̅ 𝐶 = 10
𝑋
𝑁𝐷 = 3
̅𝐷 = 0
𝑋
𝑁𝐸 = 3
̅𝐸 = 0
𝑋
𝑆2 𝐵 = 18.083
𝑆2 𝐶 = 0.375
𝑆2 𝐷 = 0
𝑆2 𝐸 = 0
13
Analysis of the mean height was done with the use of the F-test or
one-way ANOVA with a critical value of 3.48 at 0.05 level of significance.
The obtained F-test value was 6.96 which prove that there is a significant
difference among the mean height of the okra plants watered with the
different water samples (See Appendix C).
The Tukey’s Honest Significant Difference test was utilized to see
where the difference lies, using the critical value of 4.65 at 0.05 level of
significance. The resulting 𝐹𝑡 value of 1.44 showed that there is no
significant difference between the mean height of okra in the set-up C
(control group: pH 7.0) and those watered in set-up A (pH 1.0).
Comparison of the means of control group (set-up C) and set-up B
(pH 4.0) with 𝐹𝑡 value of 0.17 also showed that there is no significant
difference between the two means. The same is true with the comparison
of the means of set-up A and D and E; set-up A and B; and set-up D and
E with the 𝐹𝑡 values of 3.66, 1.61, and 0 respectively.
The statistically significant difference was found to exist between
the means of control group (Set-up C) and Set-up D and E (pH 10.5 and
14.0), with the 𝐹𝑡 value of 5.11 (See Appendix D). The same is true with
the comparison of the means of set-up B and D and E; the 𝐹𝑡 value of
5.27.
From the results, the values that surpassed the critical value in
the Tukey test mean that pH levels have a significant difference to one
another; proving that the second alternative hypothesis was correct. This
also proved the second initial hypothesis was correct as acidic pH levels
produced the optimum plant height with a 10.33 cm average and 13.5cm
individually in pH level of 4.0 compared to basic pH levels, but did not
have a significant difference with the control group.
14
Chapter V
SUMMARY, CONCLUSION AND RECOMMENDATIONS
Summary
The study aimed to compare the effect of different pH levels on A.
esculentus (okra) plant. The focus of the study is the effect on growth in
terms of growth rate and height, statistical analysis using F-test of oneway ANOVA proves that a significance difference exist between the mean
height with the obtained F-test value of 6.96 at a critical value of 3.48
and 0.05 level of significance using the Tukey test, with the critical value
of 4.65 at 0.05 level of significance, statistically significant difference was
formed to exist between the mean height of the following set-ups: 1) B
and D; 2) B and E; 3) C and D; and 4) C and E with 𝐹𝑡 values of 5.27,
5.27, 5.11, and 5.11 respectively.
Conclusion
Analysis of the results led to the following conclusions:
1. The data gathered showed support with the second alternative
hypothesis in which that pH levels does have a significant
difference on plant height with an F-test value of 6.96.
2. The results seem to support the second initial hypothesis in which
lower pH levels yielded taller plant height specifically pH levels of
4.0 and 7.0 compared to pH levels of 10.5 and 14.0 as seen in the
𝐹𝑡 values of 5.27, and 5.11 respectively.
3. A pH level of 4.0 is best to yield optimum plant height for
Abelmoschus
esculentus
(okra)
plant
as
seen
in
the
experimentation with an average of 10.33 cm and 13.5 cm in trial
2 individually.
15
4. The results lead to debunking the second alternative hypothesis
as seen that basic pH levels do not produce optimum plant height
with an average height of 0 cm.
Recommendations
By using this study as a reference, the researcher recommends the
following:
1. Use of different type of plants for more variation and comparison.
2. Use other different levels in the pH scale for more data in the
between group variance.
3. Use pots instead of plastic cups and extend experimentation
duration to have data on long-term effects of the different pH
levels.
16
BIBLIOGRAPHY
Journals
Tong, P.S. (2016). Okra (Abelmoschus esculentus) – a popular crop and
vegetable. Utar Agriculture Science Journal. Vol. 2, No 3, pp. 3941.
Books
Tiamson, M.E., Avissar, Y., Choi, J., Jurukovski, V. and Wise, R. (2015).
Plant Adaptations to Life on Land. General Biology. (pp. 218 – 219).
Open Stay College Phil. Adaptation 2016 Vibal Group.
Online Journals
Maghirang, R. G., De La Cruz, R., and Villareal, R. (2011). 4 How
Sustainable is Organic Agriculture in the Philippines [PDF]. Trans.
Nat. Acad. Sci. & Tech. (Philippines) Vol. 33 (No. 2) ISSN 01158848. p. 289 – 295
Westerfield, R. (2014). Home Garden Okra [PDF]. UGA Extension Circular
941. extension.uga.edu/publication
Online News Articles
Far Eastern Agriculture. (2012, May 8). Organic farming: The future of
Philippine
Agriculture.
Retrieved
from:
http://www.fareasternagriculture.com/crops/agriculture/organicfarming-the-future-of-philippine-agriculture
Fondriest Environmental, Inc. (2013, November 19). pH of Water.
Fundamentals of Environmental Measurements. Retrieved from:
http://www.fondriest.com/environmentalmeasurements/parameters/water-quality/ph/ >.
pH acidity: what it does to your plants. (n.d.) Retrieved from:
http://www.canna-uk.com/ph_acidity
17
Watson, K. (2016, January 26). Benefits of Okra for Diabetes. Retrieved
from: https://www.healthline.com/health/diabetes/okra#2
18
APPENDIX A
Schematic Diagram
START
Step 1:
Soak 20 seeds in 20 ml
of tap water in a bowl
for 12 hours.
Step 2:
Label each cup A1, B1,
C1, D1 and E1. Repeat
this step twice but
changing the numbers
for each trial.
Step 3:
Fill the cups with 150g
of soil with the same
pH level.
Step 5:
Adjust the pH levels
with calamansi juice or
baking
soda
accordingly per cup.
Step 6:
Water 20 ml of the
water samples to the
set-ups once, measure
& record for 14 days
for 3 trials.
Step 7:
Create tables, graphs,
organize and analyze
the data.
Step 8:
Report the results.
19
Step 4:
Sow 4 seeds per cup.
Prepare ½ cup of water
for each set-up.
APPENDIX B
Documentation
Measuring soil pH
Adjusting pH level 1.4
Adjusting pH level 10.5
Measuring 150g of soil
Adjusting pH level 4.0
Adjusting pH level 7.1
Adjusting pH level 14.1
20
DAY 1
DAY 2
DAY 3
DAY 4
DAY 5
DAY 6
DAY 7
DAY 8
21
DAY 9
DAY 10
DAY 11
DAY 12
DAY 13
DAY 14
22
APPENDIX C
Detailed Computations
F- Test
SET-UP A
SET-UP B
(1.0)
(4.0)
0 cm
5.5 cm
11.5 cm
13.5 cm
10 cm
12 cm
𝑁𝐴 = 3
𝑁𝐵 = 3
𝑋̅𝐴 = 7.17
𝑋̅𝐵 = 10.33
2
𝑆 𝐴 = 39.083
𝑆 2 𝐵 = 18.083
N= 15
k= 5
d.f.D. = 10
d.f.N = 4
Critical Value: 3.48
SET-UP C
(7.0)
10.5 cm
10.5 cm
9.5 cm
𝑁𝐶 = 3
𝑋̅𝐶 = 10
2
𝑆 𝐶 = 0.375
SET-UP D
(10.5)
0 cm
0 cm
0 cm
𝑁𝐷 = 3
𝑋̅𝐷 = 0
𝑆2𝐷 = 0
𝛼 = 0.05
𝑋̅𝐺𝑀 = 5.5
𝑆 2 𝐵 = 80.15085
𝑆 2 𝑊 = 11.5082
F-Test Value: 6.96
SET-UP E
(14.0
0 cm
0 cm
0 cm
𝑁𝐸 = 3
𝑋̅𝐸 = 0
𝑆2𝐸 = 0
(0 − 7.17)2 + (11.5 − 7.17)2 + (10 − 7.17)2
𝑆 𝐴=
= 𝟑𝟗. 𝟎𝟖𝟑
3−1
2
2
(5.5 − 10.33) + (13.5 − 10.33) + (12 − 10.33)2
𝑆2 𝐵 =
= 𝟏𝟖. 𝟎𝟖𝟑
3−1
2
2
2
(10.5 − 10) + (10.5 − 10) + (9.5 − 10)
𝑆2 𝐶 =
= 𝟎. 𝟑𝟕𝟓
3−1
2
2
2
(0 − 0) + (0 − 0) + (0 − 0)
𝑆2 𝐷 =
=𝟎
3−1
2
2
2
(0 − 0) + (0 − 0) + (0 − 0)
𝑆2 𝐸 =
=𝟎
3−1
2
̅ 𝐺𝑀 =
𝑋
𝑆2 𝐵 =
𝑆2 𝐵 =
∑ 𝑋̅ 7.17 + 10.33 + 10 + 0 + 0
=
= 𝟓. 𝟓
𝑘
5
3(7.17 − 5.5)2 + 3(10.33 − 5.5)2 + 3(10 − 5.5)2 + 3(0 − 5.5)2 + 3(0 − 5.5)2
4
320.6034
4
= 𝟖𝟎. 𝟏𝟓𝟎𝟖𝟓
𝑆2 𝑊 =
∑[(3 − 1) 39.083 + (3 − 1) 18.083 + (3 − 1) 0.375 + (3 − 1) 0 + (3 − 1) 0]
∑[(3 − 1) + (3 − 1) + (3 − 1) + (3 − 1) + (3 − 1)]
𝑆2 𝑊 =
115.082
= 𝟏𝟏. 𝟓𝟎𝟖𝟐
10
𝑆 2𝐵
80.15085
=
= 𝟔. 𝟗𝟔𝟒𝟔𝟕𝟑𝟎𝟏𝟔
𝑆 2𝑊
11.5082
23
APPENDIX D
Detailed Computations
Tukey’s Honest Significant Difference Test
Rank
1
2
3
4
5
6
7
SET- UP
Tukey Test Values 𝑭𝒕
B vs. D
B vs. E
C vs. D
C vs. E
A vs. D
A vs. E
A vs. B
A vs. C
B vs. C
D vs. E
5.27
5.27
5.11
5.11
3.66
3.66
1.61
1.44
0.17
0
𝐴 𝑣𝑠. 𝐵 = 𝑭𝒕 =
𝐴 𝑣𝑠. 𝐶 = 𝑭𝒕 =
𝐴 𝑣𝑠. 𝐷 = 𝑭𝒕 =
𝐴 𝑣𝑠. 𝐸 = 𝑭𝒕 =
𝐵 𝑣𝑠. 𝐶 = 𝑭𝒕 =
𝐵 𝑣𝑠. 𝐷 = 𝑭𝒕 =
𝐵 𝑣𝑠. 𝐸 = 𝑭𝒕 =
𝐶 𝑣𝑠. 𝐷 = 𝑭𝒕 =
𝐶 𝑣𝑠. 𝐸 = 𝑭𝒕 =
𝐷 𝑣𝑠. 𝐸 = 𝑭𝒕 =
7.17 − 10.33
√11.5082 ÷ 3
7.17 − 10
√11.5082 ÷ 3
7.17 − 0
√11.5082 ÷ 3
7.17 − 0
√11.5082 ÷ 3
10.33 − 10
√11.5082 ÷ 3
10.33 − 10
√11.5082 ÷ 3
10.33 − 10
√11.5082 ÷ 3
10 − 0
√11.5082 ÷ 3
10 − 0
√11.5082 ÷ 3
0−0
√11.5082 ÷ 3
= /−𝟏. 𝟔𝟏/
= /−𝟏. 𝟒𝟒/
= /𝟑. 𝟔𝟔/
= /𝟑. 𝟔𝟔/
= /𝟎. 𝟏𝟕/
= /𝟓. 𝟐𝟕/
= /𝟓. 𝟐𝟕/
= /𝟓. 𝟏𝟏/
= /𝟓. 𝟏𝟏/
= /𝟎/
24
Critical Value = 4.65
𝛼 = 0.05