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Running head: INFERENTIAL STATISTICS
1
Inferential Statistics:
Does Summit High School Boy Drink different Amounts of Water per Day than Girl?
Student Name
Institution
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INFERENTIAL STATISTICS 2
Introduction
Drinking sufficient water provides living things with essential nutrients required for
human survival. The subject of how much water an adult should take is controversial and lack
scientific proof until today. The United States of America dietary guidelines for the year 2015
and 2020 recommend pure drinking water than flavored water and sugar added water juices.
Many health experts advise human being to drink 2 or more liters of water in a daily for healthy
living. Similarly, Radcliffe & Watson, (2019) suggests that human beings should drink 6 up to 8
glasses of water daily irrespective of age and gender.
The National Health Service (NHS) recommends people living in hotter areas to consume
more than 8 glasses of water to avoid dehydrating. However, some people take less than 2 liters
of water in a day and look healthy irrespective of climatic and weather conditions around the
environment they live in. Even though no proven statistical research showing the relationship
between the amount of water intake by humans, age, and gender, some experts argue that infants
should drink 525ml up to 1200 ml in a day while the amount of water intake by adults between
19 and 30 years should average 2.5 liters and female and male gender should drink 2.7 and 3.7
liters of water respectively. Many people believe that water intake in human beings is dependent
on the gender of a person. Therefore, this research study aims at determining if water volume
intake in boy and girls is equal.
Hypothesis Statement
Hypothesis Word Statement
Null hypothesis: A summit high school boy drink an equal amount of water per day as a girl
Alternative hypothesis: A summit high school boy drinks a different amount of water per day
than a girl
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INFERENTIAL STATISTICS 3
Mathematical Representation
𝐻
0
: 𝜇
0
= 𝜇
1
𝐻
1
: 𝜇
0
𝜇
1
Where:
𝜇
0
- The amount of water Summit school boy drinks in a day
𝜇
1
- The amount of water a girl drinks in a day
Methodology
Data
The study utilized primary data collected from 43 secondary school students studying at
Summit school. The 30 participants were randomly sampled among students taking a statistics
course. Among the participants, 26 were female students, and 17 were male students. Moreover,
the study participants were teenagers aged between sixteen and nineteen years and whose grade
level 9 to grade 12. A questionnaire was developed where the participants were invited to
participate. Before participating in the study, all the participants were briefed about the aim of
the study, and they signed an informed consent letter.
Moreover, the confidentiality of the information the participants provided was assured
beforehand. The questionnaire prompted the participants to fill their age, gender, grade level, and
the amount of water they drink per day. The collected data was both quantitative and qualitative.
The variables “age,” “grade level,” and “water volume” were numeric while the “gender” was
qualitative. In the process of converting the qualitative data to quantitative data, “male” gender
was assigned a value of “1” while the feminine gender was assigned a value of “0”.
Data Analysis
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INFERENTIAL STATISTICS 4
To find out is a significant difference exist between the amount of water consumption
between Summit secondary school boys and girls, a two-way ANOVA model was conducted. In
the process of ANOVA analysis, the following assumptions are made:
i) The errors of the sampled data follow normal distribution
ii) Homogeneity of variances is assumed
iii) Homoscedasticity is assumed
iv) The ANOVA model assumes that each sample is independent and randomly selected
According to (Mann, 2017), a two-way ANOVA model assumes homogeneity of variances,
independence of sample data, and normal distribution of errors of sample data.
Data Output
Anova: Single
Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Gender
43
26
0.604651
0.24474
water volume
43
158
3.674419
4.03433
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
202.6046512
1
202.6047
94.69565
2.00895E-
15
3.954568
Within Groups
179.7209302
84
2.139535
Total
382.3255814
85
Mean
3.674418605
Variance
4.034330011
Error
1.205827778
Lower Interval
2.468590827
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INFERENTIAL STATISTICS 5
Upper Interval
4.880246382
Results, Interpretation, and Discussion
The results of two-way ANOVA model indicates that the calculated F statistic is 94.696
with 84 degrees of freedom and a corresponding p-value of 2.00895E-15. Using the p-value
criteria, the calculated p-value (2.00895E-15) is less than 0.05(alpha level) at 5% significance
level. Since the calculated p-value is less than alpha value, we reject the null hypothesis on the
basis that the test results are statistically sufficient. Therefore, we conclude that Summit high
school boys drink different volumes of water per day than girls.
Similarly, using the F criterion, the F critical value (94.696) is greater than the F critical
value (3.955) thus the test results are statistically significant at 𝛼 =0.05 hence we conclude that
Summit high school boys drink different volumes of water per day than girls. A 95% confidence
interval shows that the upper limit and the lower limit is 2.469 and 4.880 respectively; therefore
the average water volume intake by a person lies between 2.469 and 4.880 with 95% probability.
Conclusion
The study findings show that gender significantly affects water intake by a person. Also,
the study shows that if a person is randomly selected from a population, there is a 95%
probability that the water volume intake by a person lies between 2.469 and 4.880. In a nutshell,
males require more water intake than the female counterpart.
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INFERENTIAL STATISTICS 6
References
Mann, P. (2017). Introductory Statistics. [S.L.]: John Wiley & Sons.
Radcliffe, S., & Watson, S. (2019). Overhydration: Types, Symptoms, and Treatments. Retrieved
from https://www.healthline.com/health/overhydration

Unformatted Attachment Preview

Running head: INFERENTIAL STATISTICS 1 Inferential Statistics: Does Summit High School Boy Drink different Amounts of Water per Day than Girl? Student Name Institution INFERENTIAL STATISTICS 2 Introduction Drinking sufficient water provides living things with essential nutrients required for human survival. The subject of how much water an adult should take is controversial and lack scientific proof until today. The United States of America dietary guidelines for the year 2015 and 2020 recommend pure drinking water than flavored water and sugar added water juices. Many health experts advise human being to drink 2 or more liters of water in a daily for healthy living. Similarly, Radcliffe & Watson, (2019) suggests that human beings should drink 6 up to 8 glasses of water daily irrespective of age and gender. The National Health Service (NHS) recommends people living in hotter areas to consume more than 8 glasses of water to avoid dehydrating. However, some people take less than 2 liters of water in a day and look healthy irrespective of climatic and weather conditions around the environment they live in. Even though no proven statistical research showing the relationship between the amount of water intake by humans, age, and gender, some experts argue that infants should drink 525ml up to 1200 ml in a day while the amount of water intake by adults between 19 and 30 years should average 2.5 liters and female and male gender should drink 2.7 and 3.7 liters of water respectively. Many people believe that water intake in human beings is dependent on the gender of a person. Therefore, this research study aims at determining if water volume intake in boy and girls is equal. Hypothesis Statement Hypothesis Word Statement Null hypothesis: A summit high school boy drink an equal amount of water per day as a girl Alternative hypothesis: A summit high school boy drinks a different amount of water per day than a girl INFERENTIAL STATISTICS 3 Mathematical Representation 𝐻0 : 𝜇0 = 𝜇1 𝐻1 : 𝜇0 ≠ 𝜇1 Where: 𝜇0 - The amount of water Summit school boy drinks in a day 𝜇1 - The amount of water a girl drinks in a day Methodology Data The study utilized primary data collected from 43 secondary school students studying at Summit school. The 30 participants were randomly sampled among students taking a statistics course. Among the participants, 26 were female students, and 17 were male students. Moreover, the study participants were teenagers aged between sixteen and nineteen years and whose grade level 9 to grade 12. A questionnaire was developed where the participants were invited to participate. Before participating in the study, all the participants were briefed about the aim of the study, and they signed an informed consent letter. Moreover, the confidentiality of the information the participants provided was assured beforehand. The questionnaire prompted the participants to fill their age, gender, grade level, and the amount of water they drink per day. The collected data was both quantitative and qualitative. The variables “age,” “grade level,” and “water volume” were numeric while the “gender” was qualitative. In the process of converting the qualitative data to quantitative data, “male” gender was assigned a value of “1” while the feminine gender was assigned a value of “0”. Data Analysis INFERENTIAL STATISTICS 4 To find out is a significant difference exist between the amount of water consumption between Summit secondary school boys and girls, a two-way ANOVA model was conducted. In the process of ANOVA analysis, the following assumptions are made: i) The errors of the sampled data follow normal distribution ii) Homogeneity of variances is assumed iii) Homoscedasticity is assumed iv) The ANOVA model assumes that each sample is independent and randomly selected According to (Mann, 2017), a two-way ANOVA model assumes homogeneity of variances, independence of sample data, and normal distribution of errors of sample data. Data Output Anova: Single Factor SUMMARY Groups Gender water volume Count ANOVA Source of Variation Sum 43 26 43 158 SS df Between Groups Within Groups 202.6046512 179.7209302 1 84 Total 382.3255814 85 Average Variance 0.604651 0.24474 3.674419 4.03433 MS F 202.6047 2.139535 94.69565 95% Confidence Interval Mean Variance Error 3.674418605 4.034330011 1.205827778 Lower Interval 2.468590827 P-value F crit 2.00895E15 3.954568 INFERENTIAL STATISTICS Upper Interval 5 4.880246382 Results, Interpretation, and Discussion The results of two-way ANOVA model indicates that the calculated F statistic is 94.696 with 84 degrees of freedom and a corresponding p-value of 2.00895E-15. Using the p-value criteria, the calculated p-value (2.00895E-15) is less than 0.05(alpha level) at 5% significance level. Since the calculated p-value is less than alpha value, we reject the null hypothesis on the basis that the test results are statistically sufficient. Therefore, we conclude that Summit high school boys drink different volumes of water per day than girls. Similarly, using the F criterion, the F critical value (94.696) is greater than the F critical value (3.955) thus the test results are statistically significant at 𝛼 =0.05 hence we conclude that Summit high school boys drink different volumes of water per day than girls. A 95% confidence interval shows that the upper limit and the lower limit is 2.469 and 4.880 respectively; therefore the average water volume intake by a person lies between 2.469 and 4.880 with 95% probability. Conclusion The study findings show that gender significantly affects water intake by a person. Also, the study shows that if a person is randomly selected from a population, there is a 95% probability that the water volume intake by a person lies between 2.469 and 4.880. In a nutshell, males require more water intake than the female counterpart. INFERENTIAL STATISTICS 6 References Mann, P. (2017). Introductory Statistics. [S.L.]: John Wiley & Sons. Radcliffe, S., & Watson, S. (2019). Overhydration: Types, Symptoms, and Treatments. Retrieved from https://www.healthline.com/health/overhydration Name: Description: ...
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