Stats 1000 Statistical Practice I Assessment Answers

Answer:

Introduction

Weight gain and obesity has become a key issue for people throughout the world. This weight gain among young university or college students has become a vital concern. Furthermore, there is also increased anxiety about if weight of male and female differ from each other. It is believed that weight of female is slightly higher than male from age group of 7 to 16 but weight of male are slightly higher than weight of male after age 18, i.e. when they reach in college or university level (Halls, 2017). Furthermore in late adolescents’ years, transition from high secondary to university is critical and vulnerable period for changes in body weight and unhealthy lifestyle adoption (Vadeboncoeur, 2015). Based on this aspect, the research is going to analyse if there is difference between average weight of male and female students. Furthermore, the research is also going to analyse if there is difference in weight of students in first and second semester.

Research Design

The research is based on descriptive design. The key objective of the research is to determine the frequency of occurrence, which is in this case the weight of students. It evaluates the covariance between the variables. It is basically a longitudinal study, which involves drawing samples from population that are assessed repeatedly through time (Sreejesh, 2013).  

There are two research questions which have been analysed in the study which are:

1. Is the average weight of male students significantly higher than the average weight of female students? and
2. Is the weight of student the same during the first semester and during the second semester?

Based on the research questions, the following hypotheses are tested:

The first hypothesis of the research is:

     H₁: There is relationship between the weight of female and male students

H₀: There is no relationship between the weight of female and male students

The second hypothesis of the research is:

   H₂: There is relationship between the weight of students in first semester and second semester

  H₀: There is no relationship between the weight of students in first semester and second semester

In order to analyse the hypothesis, about 100 respondents from each sample has been observed. The hypothesis has been evaluated by using statistical measures. Bivariate tests comprising independent sample t test, paired samples t test, one way Anova, correlation and chi square test has been used in order to assess the hypothesis. Popular application MS Excel has been used in order to analyse the research questions and hypotheses. 

Results and Discussion

Analysis of First Question/Hypothesis

Independent Sample t-Test

The following table demonstrates the independent sample t test of the variables:

From the above table, it can be observed that the mean weight of male students’ weight is 73.27 and mean value of female students’ weight is 58.24. The value of t statistics is 0.00 which is less than the P value at 0.05, i.e. T<0.05. Therefore, it can be stated that the samples means are statistically significantly different (Heiman, 2010). Furthermore, on the basis of the analysis, it can be stated that the average weight of male students are significantly higher in comparison with the average weight of female students.  

Anova Single Factor Analysis

The following tables demonstrates Anova single factor analysis of the variables

From the above table, it can be observed that P value is 5.3E – 16 which is less than the significance level of 0.05, i.e. P<0.05. Thus, from this analysis also it can be stated that the differences of means are statistically significant (Peck, 2015).  

Correlation

The following table demonstrates the correlation analysis between the variables  

From the above analysis, it can be observed that value of correlation coefficient between male student’s weight and female students’ weight is 0.869 which is positive and much closer to 1 (Sharma, 2007). Thus, it can be stated that strong positive relationship exist between the variables, i.e. increase in male students’ weight is related with increase in female student’s weight.    

Chi Square Test

The following table demonstrates the chi square test between the variables:  

From the above analysis, it can be observed that the value of Chi square is 1724, i.e. X(1) = 1724. This tells that there is statistically significant relationship between male students’ weight and female students’ weight (PennState Eberly College of Science, n.d.).  

On the basis of the statistical analysis, the first null hypothesis is rejected and first alternate hypothesis is accepted. Thus, it can be concluded that there is relationship between weight of male students and weight of female students.   

Analysis of Second Question/Hypothesis

Paired Samples t-Test

The following table demonstrates the paired samples t-test of the variables

From the analysis, it can be observed that mean values of weight of students in second semester and first semester are 65.76 and 66.67 respectively. The value of t statistics is derived as 0.014 which is less than the P value of 0.05, i.e. T<0.05. Thus, it can be stated that samples mean are statistically significantly different.      

Anova Single Factor Analysis

The following table demonstrates Anova single factor analysis of the variables

From the above analysis, it can be observed that P value is 0.513, which is more than the significance level of 0.05, i.e. P>0.05. Thus, on the basis of analysis, it can be concluded that the differences of means between the variables are statistically insignificant. Hence, on the basis of the analysis, it can be concluded that there is no differences in the weight of students in first and second semester. Thus, it can be stated that the weight of students are almost similar during the first semester and during the second semester.  

Correlation

The following table demonstrates the correlation analysis between the variables:

From the above analysis it can be observed that the value of correlation coefficient between the variables is 0.931 which is positive and much closer to 1. Thus, it can be stated that strong positive relationship exist between the variables, i.e. increase in weight in first semester is related with increase in the weight of second semester among the students.    

Chi Square Test

The following table demonstrates the chi square test between the variables

From the above analysis, it can be observed that the value of chi square is 4650, i.e. X(1) = 4650. This states that there exist statistically significant relationship between the weight of students in first semester and second semester.

Thus, on the basis of the analysis, the second null hypothesis is rejected and alternate hypothesis is accepted. Hence, it can be stated that there is relationship between the weight of students in first semester and second semester.

Conclusion

The key findings obtained from the research are that the average weight of male students is higher than average weight of female students. Furthermore, there exist certain relationship between male students’ weight and female students’ weight. On the other hand, it has also been found that weight of students is quite similar between first and second semester.  Besides, certain positive relationship has also been found between the weights of students in both semesters. This research calls for better analysis and quality of reporting with respect to weight gain. Reported information should be presented with standard deviation for properly interpreting the findings. Moreover, beyond the overall weight changes, the proportion of students gaining weight require to be reported for better evaluation.

References

Halls. (2017). What is BMI? Retrieved from https://halls.md/bmi-difference-men-women/

Heiman, G. (2010). Basic Statistics for the Behavioral Sciences. Cengage Learning.

Peck, R. (2015). Introduction to Statistics and Data Analysis. Cengage Learning.

PennState Eberly College of Science. (n.d.). 4.0 - Chi-Square Tests. Retrieved from https://onlinecourses.science.psu.edu/statprogram/node/158

Sharma, J. K. (2007). Business Statistics. Pearson Education India.

Sreejesh, S. (2013). Business Research Methods: An Applied Orientation. Springer Science & Business Media.

Vadeboncoeur, C. (2015). A meta-analysis of weight gain in first year university students: is freshman 15 a myth? BMC Obesity, 2(22), 1-9.