The statistical analysis plays an important role in the process of decision making. We make decisions based on the statistical analysis for the available data. Here, we have to want to analyze the data for yearly expense for the Australian students on Food and beverages. For this study, we have to use the statistical tools and techniques. We have to check some claims or hypotheses regarding the yearly expense of the Australian students on the food and beverages. For checking these claims we have to use testing of hypothesis or inferential statistics. Let us see this statistical analysis in detail explained in the next topics.
It is very important to establish the research hypotheses or claims for any type of research study. For this research study, the research questions or hypotheses are established as below:
Whether there is any significant difference in the average expenditure for Australian students with different education levels?
Whether the average expenditure for the male and female students is same or not?
Whether the expenditure is independent of gender of the student or not?
It is very important to collect the data for checking the different research hypotheses or claims. Data collection is the primary step for any research study. Without data collection we cannot prove or check the given hypotheses or claims regarding the different variables involved in the research study. For this research study we have to collect the data for checking above established hypotheses. The process of data collection would not contain any biases which may produce the biased results. For checking the above established hypotheses or claims, we need to collect the data and then test this data for checking these hypotheses. The data for this study is collected for 351 randomly selected students including males and females. Data is collected for the three variables such as expenditure in AU$, education of the student, and gender of the student. By using this data we have to check the above stated claims or hypotheses. Data is collected by using the proper methods of random sampling and data includes the male and female. All types of different biases are avoided during the process of data collection for getting unbiased results for this research study.
Statistical analysis is very important for the process of decision making. We have to use the descriptive statistics, graphical analysis, inferential statistics or testing of hypothesis for this research study. We have to check the above stated hypotheses by using the testing of hypotheses. We have to use the one way analysis of variance or ANOVA test for checking whether there is any significant difference in the average expense of Australian students with different education levels. Also, we have to use the two sample t test for the population mean for checking the hypothesis whether there is any significant difference in the average expense for the male and female students. Also, we have to use the Chi square test for independence of two categorical variables for checking whether the expense of student and gender of student is independent from each other or not. By using the descriptive statistics we get the general idea about the nature of data and spread of data.
By using the descriptive statistics, we get the general idea about the nature of the data. We can easily check the spread of the data and variation in the data by observing the descriptive statistics. The value of the minimum and maximum provides us the range for the given variable under study. The use of descriptive statistics is also useful for comparing the results. We can compare the same variable for different factors or different periods or places.
The average expenditure of the students is given as AU$10116 with the standard deviation of AU$ 660. The minimum expenditure is observed as AU$9000 while the maximum expenditure is observed as AU$11297.
|
Descriptive Statistics |
||||||
|
N |
Range |
Skewness |
Kurtosis |
|||
|
Statistic |
Statistic |
Statistic |
Std. Error |
Statistic |
Std. Error |
|
|
Expenditure_$ |
351 |
2297.00 |
.124 |
.130 |
-1.198 |
.260 |
|
Valid N (listwise) |
351 |
The coefficient of skewness for the data for variable expenditure is given as 0.124, which means the data for the variable expenditure is skewed at right side or the data for expenditure is positively skewed. The coefficient of kurtosis is given as -1.198, which means data for the expenditure is platykurtic. From the above table, it is observed that the data for the expenditure is positive skewed.
From above box plot, it is observed that the data for expenditure is positive skewed.
From the given histogram, we conclude that the given data does not follow a normal or approximately normal distribution.
Now, we have to see the frequency distribution for the level of education which is given as below:
|
Education |
|||||
|
Frequency |
Percent |
Valid Percent |
Cumulative Percent |
||
|
Valid |
High School or lower |
85 |
24.2 |
24.2 |
24.2 |
|
Under-Graduate |
90 |
25.6 |
25.6 |
49.9 |
|
|
Graduate |
93 |
26.5 |
26.5 |
76.4 |
|
|
Post-graduate or more |
83 |
23.6 |
23.6 |
100.0 |
|
|
Total |
351 |
100.0 |
100.0 |
It is observed that about 85 respondents in the given study have the education as high school or lower, about 90 respondents have education as under-graduate, about 93 respondents have the education as graduate, while about 83 respondents have their education as post-graduate or more. The proportion for the respondents who have education as post graduate or more is given as 23.6%. The percentage of the graduate respondents is given as 26.5%. The percentage of under graduate respondents are given as 25.6% while the percentage of the respondents with high school or lower education is given as 24.2%.
From above table, it is observed that the data consist of approximately equal proportion of the students with four different education levels.
Now, we have to see the frequency distribution for the gender of the students which is given as below:
|
Gender |
|||||
|
Frequency |
Percent |
Valid Percent |
Cumulative Percent |
||
|
Valid |
Male |
163 |
46.4 |
46.4 |
46.4 |
|
Female |
188 |
53.6 |
53.6 |
100.0 |
|
|
Total |
351 |
100.0 |
100.0 |
The proportion of the male respondents in the given data set is 46.4% while the percentage of the female respondents in the given data set is 53.6%.
From above table, it is observed that data contains 163 males and 188 females.
Now, we have to check whether there is any significant difference in the average expense for the students with different education levels or not.
The box plots for comparison of the average expense with four different education levels are given as below:
#SAS COMMANDS
>title ‘Box Plot for Expenditure by Education’;
>proc boxplot data=Expenditure;
>plot Expenditure*Education;
> inset min mean max stddev /
>header = ‘Overall Statistics’
>pos = tm;
insetgroup min max /
>header = ‘Expenditure by Education’;
>run;
From the above box plots, it is observed that there is a significant difference in the average expense for the students with four different education levels. For the under graduate respondents, there is a more variation observed as compared to other respondents.
Now, we have to see the box plots for the average expense for the male and female students which are given as below:
#SAS COMMANDS
>title ‘Box Plot for Expenditure by Gender’;
>plot Expenditure*Gender;
>inset min mean max stddev /
>header = ‘Overall Statistics’
>pos = tm;
>insetgroup min max /
>header = ‘Expenditure by gender’;
>run;
From the above box plots, it is observed that there is no any significant difference observed in the average expense for the male student and female student.
Now, we have to check the claim whether there is any significant difference in the average expense for the students with different education levels or not. For checking this claim or hypothesis, we have to use the one way analysis of variance or ANOVA. The null and alternative hypothesis for this test is given as below:
Null Hypothesis: H0: There is no any significant difference in the average expense of the students with different education levels.
Alternative hypothesis: Ha: There is a significant difference in the average expense of the students with four different education levels.
For this test we assume the level of significance or alpha value as 0.05.
Descriptive statistics for the expenses for the students with four different education levels is summarised as below:
The ANOVA table for this test is given as below:
#SAS COMMANDS:
>proc anova data = Expenditure;
>class Education;
>model Expenditure = Education;
>run;
For this ANOVA test, we get the p-value as 0.548 which is more than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that there is no any significant difference average expense of the students with different education levels. This means we conclude that there is no any significant difference average expense of the students with different education levels.
Now, we have to check another claim or hypothesis whether there is any significant difference in the average expenditure between the male and female student. For checking this hypothesis we have to use two sample t test for the population mean. The null and alternative hypothesis are given as below:
Null hypothesis: H0: There is no any significant difference in the average expenditure between the male and female student.
Alternative hypothesis: Ha: There is a significant difference in the average expenditure between the male and female student.
The test is given as below:
For this test we get the p-value as 0.466 which is greater than the level of significance or alpha value 0.05. So, we do not reject the null hypothesis that there is no any significant difference in the average expenditure between the male and female student.
Now, we have to check the claim whether the gender and education of the student is independent from each other or not. We have to use the Chi square test for checking this hypothesis. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: The gender and education of the student is independent from each other.
Alternative hypothesis: Ha: The gender and education of the student is not independent from each other.
The cross tabulation and calculations for this test is given as below:
Test statistic
Chi square = ∑[(O – E)^2/E]
Where O = observed frequencies and E is expected frequencies
Expected frequencies are calculated as below:
E = Row total*Column total / Grand total
We get p-value as 0.065 which is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that the gender and education of the student is independent from each other.
There is sufficient evidence to conclude that the gender and education of the student is independent from each other.
Conclusions
The average expenditure of the students is given as AU$10116 with the standard deviation of AU$ 660. The minimum expenditure is observed as AU$9000 while the maximum expenditure is observed as AU$11297.
There is sufficient evidence to conclude that there is no any significant difference average expense of the students with different education levels.
There is sufficient evidence to conclude that there is no any significant difference in the average expenditure between the male and female student.
There is sufficient evidence to conclude that the gender and education of the student is independent from each other.For the under graduate respondents, there is a more variation observed as compared to other respondents.
References
Evans, M. (2004). Probability and Statistics: The Science of Uncertainty. Freeman and Company.
Hastle, T., Tibshirani, R. and Friedman, J. H. (2001). The elements of statistical learning: data mining, inference, and prediction: with 200 full-color illustrations. Springer – Verlag Inc.
Hogg, R., Craig, A., and McKean, J. (2004). An Introduction to Mathematical Statistics. Prentice Hall.
Liese, F. and Miescke, K. (2008). Statistical Decision Theory: Estimation, Testing, and Selection. Springer.
Pearl, J. (2000). Casuality: models, reasoning, and inference. Cambridge University Press.
Ross, S. (2014). Introduction to Probability and Statistics for Engineers and Scientists. London: Academic Press.
https://data.oecd.org/eduresource/education-spending.htm
https://future-students.uq.edu.au/international/cost-living
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