Posted: June 13th, 2022

4. Assignment: Is There a Difference?

Getting Started
You have come up with a great new idea for a product and are thinking about starting your own business. Your idea is an automatic pet groomer! We have robotic carpet vacuums, why not one that every six weeks or so bathe, cuts hair, and trim nails for the household pet!
You have solved the technical problems, but are not sure if it is economically feasible. Your analysis suggests that if the average citizen of the nearest major city to you spends at least $ 100 every three months on pet grooming your product will be an enormous success. You have conducted a survey to gather data, but do not know what to do next. In this workshop, you will learn how to create hypotheses for research testing and how to test those hypotheses about the population. Using these methods, you can see if your idea has any potential or not
Upon successful completion of this assignment, you will be able to:
Make statistical comparisons between data sets.
Background Information
As you were thinking about your hopeful new business, it occurred to you that the nearest city to you may not be the best place, that some other city might be a better place to start this business. So in addition to the data on your nearest city, you also collected data from another larger city in your region. Comparing two or more sets of data is a common task in data analytics. In this workshop, you will learn how to write hypotheses, and also learn how to examine data between two different variables. So using these techniques, you may be able to make an informed decision concerning the viability of your new business opportunity and if one city is better than the other
Instructions
Review the rubric to make sure you understand the criteria for earning your grade.
Read chapters XI, and XII, and XIII in the onlinetextbook. Watch the videos and powerpoints that go with each chapter.
Examine the NCbirthsdatabase. Pick three of the following research questions:
Is there a relationship between a mother’s age and the birth weight of her child?
Is there a relationship between whether a mother smokes or not and the birth weight of her child?
Is the birthweight of babies from white moms different than those from nonwhite moms?
Is there a relationship between the mother’s weight gain during pregnancy and the birth weight of her child?
Is there a relationship between the mother’s marital status and the birth weight of her child?
Is there a relationship between the mother’s age and her marital status?
Is there a relationship between the father’s age and the mother’s marital status?
Find two published articles dealing with each of your selected questions. Write a one-paragraph summary of what each article says about your research question.
Determine the mean, median, mode, standard deviation, and variance as applicable for the variables involved in your study. Provide a graphical analysis for the variables that cannot have numerical statistics calculated.
Determine the type of test you will use for each of your research questions and the null and alternative hypothesis for each question.
Conduct the appropriate statistical tests at the .05 significance level.
Write a short report ( 1 to 2 pages for each research question) that includes the results of your analysis. Present the results and discuss the implications of your findings. Include whatever graphs or statistical output you may have generated in answering these questions along with a short explanation of your analysis.Are your results consistent with the published research on the topic?Why or why not?
When you have completed your assignment, submit a copy to your instructor using the Assignment submission page.
The assignment is due by the end of the workshop.
informationSYSTEMS
ATTACHED FILE(S)
6/11/22, 8:09 AM Preview Rubric: 4.2 Assignment: Is There a Difference? (75 points) – 3SU2022 Data Analytics & Research (BADM-707-01B) – Indiana Wesley…
https://brightspace.indwes.edu/d2l/lp/rubrics/preview.d2l?ou=165060&rubricId=518401&originTool=quicklinks 1/4
4.2 Assignment: Is There a Difference? (75 points)
Course: 3SU2022 Data Analytics & Research (BADM-707-01B)
Criteria Excellent Competent
Needs
Improvement
Inadequate/Faili
ng
Criterion Score
Determination
of test
hypothesis
and selection
of test
/ 20
Statistical
tools
/ 20
20 points
Demonstrated
clear, insightful
critical thinking
in determining
the test
hypothesis and
selection of
test.
19 points
(16-19 points)

Demonstrated
competent
critical thinking
in determining
the test
hypothesis and
selection of
test
15 points
(12-15 points)

Demonstrated
limited critical
thinking in
determining
the test
hypothesis and
selection of
test
11 points
(0-11 points)

demonstrated
little to no
critical thinking
in determining
the test
hypothesis and
selection of
test
20 points
Statistical tools
were
constructed
correctly and
strongly
supported the
discussion.
18 points
(16-18 points)

Statistical tools
were
constructed
correctly and
generally
supported the
discussion.
15 points
(12-15 points)

Statistical tools
were
constructed
correctly and
but did not
support the
discussion.
11 points
(0-11 points)

Statistical tools
were not
constructed
correctly but
did not
support the
discussion.
6/11/22, 8:09 AM Preview Rubric: 4.2 Assignment: Is There a Difference? (75 points) – 3SU2022 Data Analytics & Research (BADM-707-01B) – Indiana Wesley…
https://brightspace.indwes.edu/d2l/lp/rubrics/preview.d2l?ou=165060&rubricId=518401&originTool=quicklinks 2/4
Criteria Excellent Competent
Needs
Improvement
Inadequate/Faili
ng
Criterion Score
Discussion of
your findings
and comparing
it to published
research
/ 2020 points
Demonstrated
clear, insightful
critical thinking
in the
Discussion of
the findings
and comparing
it to published
research.
19 points
(16-19 points)

Demonstrated
competent
critical thinking
in the
Discussion of
the findings
and comparing
it to published
research.
15 points
(12-15 points)

Demonstrated
limited critical
thinking in
Discussion of
the findings
and comparing
it to published
research.
11 points
(0-11 points)

Demonstrated
little to no
critical thinking
in the
Discussion of
the findings
and comparing
it to published
research.
6/11/22, 8:09 AM Preview Rubric: 4.2 Assignment: Is There a Difference? (75 points) – 3SU2022 Data Analytics & Research (BADM-707-01B) – Indiana Wesley…
https://brightspace.indwes.edu/d2l/lp/rubrics/preview.d2l?ou=165060&rubricId=518401&originTool=quicklinks 3/4
Total / 75
Criteria Excellent Competent
Needs
Improvement
Inadequate/Faili
ng
Criterion Score
Grammar,
Spelling,
Length, and
Citation
/ 1515 points
Sentence
structure is
complete with
correct
spelling,
punctuation,
capitalization,
varied diction,
and word
choices.

Assignment
length is
correct with
sources
correctly cited.
14 points
(12-14 points)

Sentence
structure has
minor errors
(fragments,
run-ons) with
correct
spelling,
punctuation,
capitalization,
and limited
diction and
word choices.

Assignment
length is
correct with
sources
correctly cited.
11 points
(9-11 points)

Sentence
structure has
several errors
in sentence
fluency with
multiple
fragments/run-
ons; poor
spelling,
punctuation,
and/or word
choice.

Assignment
length is
inappropriate
with several
format and
citation errors.
8 points
(0-8 points)

Sentence
structure has
serious and
persistent
errors in
sentence
fluency,
sentence
structure,
spelling,
punctuation,
and/or word
choice.

Assignment
length is
inappropriate
with several
format and
citation errors
or sources not
cited.
6/11/22, 8:09 AM Preview Rubric: 4.2 Assignment: Is There a Difference? (75 points) – 3SU2022 Data Analytics & Research (BADM-707-01B) – Indiana Wesley…
https://brightspace.indwes.edu/d2l/lp/rubrics/preview.d2l?ou=165060&rubricId=518401&originTool=quicklinks 4/4
Overall Score
Excellent
69 points minimum
Competent
62 points minimum
Needs Improvement
54 points minimum
Inadequate/Failing
0 points minimum
1
Data Analytics and Research 2
Data Analytics and Research:
4.2 Assignment
Data Analytics & Research
Research Question Selection
1) Is there a relationship between whether a mother smokes or not and the birth weight of her child?
2) Is the birth weight of babies from white moms different than those from non-white moms?
3) Is there a relationship between the mother’s weight gain during pregnancy and the birth weight of her child?
Question 1
Is there a relationship between whether a mother smokes or not and the birth weight of her child?
For the first part we find two articles dealing with the above research question and provide a summary of each article:
Article 1
The behaviour of infants whose mothers smoke in pregnancy
The behavior of infants whose mothers smoke in pregnancy by David Saxton
In this study, the author compares the infants of mothers who had smoked more than 15 cigarettes/day throughout their pregnancy and the infants whose mothers did not smoke. The author observes that all the infants were spontaneously delivered at the end of the pregnancy term and they were of normal birth weight. The author also matches the two groups for maternal age, social class and parity. The author observes that the duration of labour and analgesia during labour were similar for mothers who smoked and the mothers who were not smokers. Although the author does not observe any significance effect in the birth weight of infants due to smoking, he finds evidence to suggest the child’s auditory senses could be affected by the mother smoking during pregnancy (Saxton, 1978).
Article 2
Maternal smoking and birthweight
The study was aimed to find if mother’s smoking during pregnancy affected the birthweight of the child. The data collected and analysed was of 1016 pairs of births that occurred in 1946- 1963 in Washington County, Maryland. The author examines the mean birth weight of first and second members of pairs of consecutive births of the same mother with respect to her smoking habits. He concludes no significant difference in the birth weight of the infants in which the mother was a smoker in both or either of the two pregnancies (Silverman, 1977). But the author observes that the birth weights of the infants of women who were non-smokers throughout both pregnancies was higher than that of infants of women who smoked during both pregnancies. He also observes that the infants of first members of pairs in which the mothers smoked only during the second pregnancy tended to have birth weights which were lower than that of infants of non-smokers and higher than that of infants of smokers (Silverman, 1977). Hence, he concludes that these findings neither confirm nor deny the hypothesis that smoking during pregnancy causes a reduction in birth weight of the infant.
Analysis
Now for analysing our data we find the mean, median, mode, variance and the standard deviation of our data in the table below:

Birth weight of the child
Mother Smoking

Birth weight of the child
Mother Non-Smoking

Mean
Median
Mode
Variance
Standard Deviation

7.144273
7.31
7.44
2.303749
1.517811

6.82873
7.06
7.31
1.906244
1.380668
Now we do the statistical tests to see if there is any correlation between the two populations. Let the populations non-smoking mother and Smoking Mother be A and B respectively. Letandbe the total number in both the populations.
Now,
Null Hypothesis: The difference in the population means, .
Alternate Hypothesis: .
We are going to conduct the test in the 0.05 level of significance. The degrees of freedom for our population, df = n-1 where n is the minimum ofand . Here we are going to conduct the two tailed student’s t test. Firstly, for our populations A and B we calculate the t- value usingwhereis the mean of the population A andis the mean of the population B, is the variance of population A andis the variance of the population B andis the total number of values in population A andis the total number of values in population B.
After calculation, we get t = 1.809311. We use a t- distribution calculator to find the p- value for the null hypothesis to be true, p = 0.072807 which is greater than our significance value 0.05. Hence, we conclude that our alternate hypothesis is not significant at the 0.05 significance level. We do not claim that our null hypothesis to be true. We do not have sufficient data to conclude that.
Question 2
Is the birth weight of babies from white moms different than those from non-white moms?
For the first part we find two articles dealing with the above research question and provide a summary of each article:
Article 1
Birth weight of US biracial (black-white) infants: regional differences
The author examines the prevalence of low birth weight among biracial infants (black mother-white father vs. white mother-black father) in different regions of United States using the data base in 1991. He observes that the rate of low birth weight was 31% higher in the black mother and white father group than in the white mother and black father group (Polednak & King, 1998). He also observes that the difference was smaller in the Northeast United States, is larger in the Western United States. He concludes that there is prevalence of low birth weight among biracial infants and that more studies are needed to identify the maternal factors involved in the regional difference.
Article 2
Diverging associations of maternal age with low birthweight for black and white mothers
In United States, studies suggest a risk of low birth weight increases more quickly with maternal age for black women than it does for white women. The aim was to study the above statement. They take the birth data in Chicago from 1994 to 1996. They study the link between maternal age with risk of low birth weight with respect to maternal race/ethnicity, marital status, education, and neighbourhood poverty of the mothers (Rich-Edwards et al., 2003). In their findings, they see the risk of low birthweight rose steeply with maternal age for black, but not white, mothers. After making the data bit adjusted by considering various other factors, they conclude that the risk of low birth weight rises more quickly with maternal age for women who are disadvantaged, regardless of their race and ethnicity. They conclude that the particularly steep increase in risk of low birth weight with increasing maternal age for black women is due to the high prevalence of disadvantaged women in this population (Rich-Edwards et al., 2003).
Analysis
Now for analysing our data we find the mean, median, mode, variance and the standard deviation of our data in the table below:

A
Birth weight of child
White mother

B
Birth weight of child
Non-white mother

Mean
Median
Mode
Variance
Standard Deviation

7.172539683
7.47
7.56
2.575158629
1.60473008

6.75404762
6.845
6.75
2.94240346
1.71534354
We will use the student’s t test to see if there is any correlation between the two populations.
Our Null Hypothesis will be: The difference in the population means is 0, that is
And the Alternate Hypothesis will be:
We are going to conduct the test in the 0.05 level of significance. HenceThe degrees of freedom for our population, df = n-2 where n is the minimum ofand . Here we are going to conduct the two tailed student’s t test. Firstly, for our populations A and B we calculate the t- value using the following formula whereis the mean of the population A andis the mean of the population B, is the variance of population A andis the variance of the population B andis the total number of values in population A andis the total number of values in population B. After putting in the values in the formula, we get t =. Now, the next step is to calculate the probability value or p value for the null hypothesis to be true. We use the t- distribution calculator to find the p- value which turns out to be less than significance value.
Now we do the statistical tests to see if there is any correlation between the two populations. Let the birth weights of the white mother and non-white mother be A and B respectively. Letandbe the total number in both the populations.
Now,
Null Hypothesis: The difference in the population means, .
Alternate Hypothesis: .
We are going to conduct the test in the 0.05 level of significance. The degrees of freedom for our population, df = n-1 where n is the minimum ofand . Here we are going to conduct the two tailed student’s t test. Firstly, for our populations A and B we calculate the t- value usingwhereis the mean of the population A andis the mean of the population B, is the variance of population A andis the variance of the population B andis the total number of values in population A andis the total number of values in population B.
After calculation, we get t = 2.58579949. We use a t- distribution calculator to find the p- value for the null hypothesis to be true, p = 0.010218 which is which is less than our significance value 0.05. Hence, we reject our null hypothesis. And we conclude that our alternate hypothesis is significant at the 0.05 significance level. We see that our results match with the results of the articles we reviewed. It could be because we got our p-value around 0.01 which is very much lesser than our significance value 0.05.
Question 3
Is there a relationship between the mother’s weight gain during pregnancy and the birth weight of her child?
For the first part we find two articles dealing with the above research question and provide a summary of each article.
Article 1
The association between pregnancy weight gain and birthweight: A within-family comparison
The authors aim to examine the association between maternal weight gain and birthweight using state-based birth registry data. They use the data of births in Michigan and New Jersey, USA, between Jan 1, 1989, and Dec 31, 2003. From their data they excluded the following data points, 1) gestation less than 37 weeks or 41 weeks or more 2) maternal diabetes 3) birthweight less than 500 g or more than 7000 g and 4) those women whose data for pregnancy weight gain was missing. On their analysis, they find a consistent link between pregnancy weight gain and birthweight. They observe that the infants of women who gained more than 24 kg during pregnancy were 148·9 g heavier at birth than were infants of women who gained 8-10 kg (Ludwig & Currie, 2010). They conclude that the maternal weight gain during pregnancy increases birthweight independent of the genetic factors.
Article 2
Gestational weight gain and its relationship with the birthweight of offspring
The authors aim to study the relationship between the weight gain during pregnancy ang the birthweight of the offspring. Data of child births from Beijing Obstetrics and Gynecology Hospital and Haidian Maternity and Child Health Care Hospital in 2010 were used for the study. And they observed only singleton pregnancies. All the pregnant women were divided into underweight, normal weight and overweight group (Wang et al., 2013). They defined the Birthweight between 2500 g and 4000 g as normal birthweight, and 2900 g to 3499 g as appropriate birthweight. They divided the population into different groups and explored were used it to analyse the gestational weight gain (GWG). After researching the data for all the diferent groups using appropriate statistical analysis, they conclude the mother’s weight gain during pregnancy is positively related to the child’s birth weight (Wang et al., 2013).
Analysis
Now for analysing our data we find the mean, median, mode, variance and the standard deviation of our data in the table below:

Mother’s weight gain during pregnancy
(x)

Birth weight of the child
(y)

Mean
Median
Mode
Variance
Standard Deviation

30.3258
30
30
202.6061
14.23398

7.119507
7.31
7.44
2.220635
1.49018
Here we are going to conduct the two tailed student’s t test. We will use the student’s t test to see if there is any correlation between the two populations.
Null Hypothesis: The population correlation coefficient
Alternate Hypothesis: The population correlation coefficient
The degrees of freedom for our population, df = n-2 = 998 -2 = 996. Firstly, for our variables x and y, we calculate the population correlation coefficient,
.
By calculating, we get r = 0.154171555.
Now for the t-value, we use the formula
where r is the sample correlation coefficient we computed in the previous step and n is the total number in the sample. Now the next step is to calculate the probability value or. By using t- distribution calculator we find that the p value for the null hypothesis to be true is, p < .00001. We can see that it is less than our significance value 0.05. Hence we reject our null hypothesis. And we conclude that our alternate hypothesis is significant in our given significance level. We see that our results match with the results of the articles we reviewed. It could be because we got our p-value around 0.01 which is very much lesser than our significance value 0.05. References Ludwig, D. S., & Currie, J. (2010). The association between pregnancy weight gain and birthweight: a within-family comparison.The Lancet,376(9745), 984-990. Polednak, A. P., & King, G. (1998). Birth weight of US biracial (black-white) infants: regional differences.Ethnicity & disease,8(3), 340-349. Rich-Edwards, J. W., Buka, S. L., Brennan, R. T., & Earls, F. (2003). Diverging associations of maternal age with low birthweight for black and white mothers.International journal of epidemiology,32(1), 83-90. Saxton, D. W. (1978). The behaviour of infants whose mothers smoke in pregnancy.Early human development,2(4), 363-369. SilvermanD.T. (1977).Maternalsmokingandbirthweight.AmJEpidemiol, 105, 513-21. Wang, W. P., Chen, F. F., Mi, J., Teng, Y., Zhao, J., Wu, M. H. & Teng, H. H. (2013). Gestational weight gain and its relationship with the birthweight of offspring.Zhonghua fu chan ke za zhi,48(5), 321-325.

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