a.The article based on the analysis of public transport system. The data for the study has been provided by transport for NSW, the provided data is a subset of opal tap on and tap off location between 8thto 14th August 2016 in Australia.
Consider the article “Transport systems and their impact con gender equity”,
(https://www.sciencedirect.com/science/article/pii/S2352146517305355), the analysis shows that there are variances in transport convenience between men and women, and women have less accessibility because of the higher travel times and percentage of income spent in transport. In the higher income regions, men and women mark comparable number of journeys per day and spend comparable percentages of their income. Also, it was exciting to see that, women chose cheapest mode, and at whatever time possible, women preferred the private vehicle like car or taxi among the public transport modes.
The requirement of the study is to provide the recommendations to improve public transport system. So, business question can be assume as, is there a significance difference between the proportions of particular mode of transport.
The data collection can be divided into two types, the first one is Primary data, which collected directly from the employees on the basis of designed questionnaire. The other one is Secondary data, which collected from some other resources according to the requirement of analysis. (Goodwin, 2012).
The dataset 1 has been provided by transport for NSW, it is a subset of opal tap on and tap off location between 8th to 14th August 2016 in Australia. Thus, dataset 1 is collected by other source. Hence, it is a secondary data.
The collected data can be further categorized as qualitative or quantitative measurements, the qualitative data contains the values for the ordinal level and the nominal level of measurements.
And, the quantitative data contain the values of interval or ratio level measurements. (Morgan, 2013)
The dataset-1 contains data of 1000 peoples which have 5 variables that are as follows:
The dataset2 is collected by 40 working people, which is greater than sample size 30. Thus, the results obtained from the study will not be biased. The variable mode indicated the type of public transport which are Bus, Train, Ferry and Light Rail indicated by the variable mode. The variable mode has divided into four categories, so it will be nominal level variable.
The variable tap specifies the tap type which has divided into 2 categories (on and off), so it is a nominal level variable. The variable gender specifies the type of gender which has divided into 2 categories (male or female), so it is a nominal level variable.
The numerical for the type of public transport is shown below:
|
Row Labels |
Count of mode |
Percentage of mode |
|
bus |
463 |
46.30% |
|
ferry |
19 |
1.90% |
|
lightrail |
15 |
1.50% |
|
train |
503 |
50.30% |
|
Grand Total |
1000 |
According to the above numerical summary, out of 1000 times, buses was used 463 times, trains was used 503 times, ferry was used 19 times and lightrail was used 15. The people mostly prefer the train (50.30%) and the bus (46.30%) for the public transport. Thus, train was most used by the NSW people during 8th to 14th of August 2016.
The graphical summary is shown below:
According to the above pie chart for the public transport mode, train was most used about 50% of the time, bus was used about 46% of the time, lightrail was used 2% of the time and ferry was used 2% of the times by the NSW people during 8th to 14th of August 2016.
Hence, train was most used by the NSW people during 8th to 14th of August 2016.
The single proportion test is used to compare a proportion in one group to identify the population proportion. The null hypothesis and the alternate hypothesis for the one -tailed test are given as below:
The statistic for the test is given as below:
Here, the sample proportion for the most used by the NSW people during 8th to 14th of August 2016 is 48.5%. So, the value of the test statistic is calculated as:
Now use, the standard normal probability table for one tailed test, the p-value is about 0.425.
From the results, it is observed that p-value is 0.425. Now, compare the p-value with level of significance say 0.05. As p-Value > level of significance (0.05), the null hypothesis is accepted and thus there is sufficient evidence to conclude there are more than 50% of public transport users in NSW use the train mode of transport found in Part a.
Thenumerical summary for the variables location, by only considering those three stations (Bankstown Station, Gosford Station and Parramatta Station) ; and the variable count by considering the data with trains only is shown below:
|
mode |
train |
||
|
Row Labels |
Count of count |
Average of count2 |
Sum of count3 |
|
Bankstown Station |
5 |
153.2 |
766 |
|
Gosford Station |
6 |
40 |
240 |
|
Parramatta Station |
5 |
825.8 |
4129 |
|
Grand Total |
16 |
320.9375 |
5135 |
According to the above pivot table analysis, the Parramatta station have mostly tapped on/off. The average number of tap on/off is 825.8 and total count of tap on/off are 4129.
The graphical summary for the variables location, by only considering those three stations (Bankstown Station, Gosford Station and Parramatta Station) ; and the variable count by considering the data with trains only is shown below:
Thus, Parramatta station have mostly used, so government can build underground railway station from Parramatta station to central.
Analysis of variance is used to test more than two sample means measured in quantitative level of measurements. (Maxwell Roberts and Riccardo Russo, 2014).
The one way analysis of variance is used to tests whether there is significant relationship between the means of unrelated groups which have more than two levels.
The two way analysis of variance is used to tests whether there is significant relationship between the two unrelated groups which has more than two levels.
The null hypothesis is: The mean for all groups is equal.
And, the alternative hypothesis is: At least one of the mean is different from another.
The calculations has been done in STATKEY, the summary results for the three stations by using Statkey is shown below:
n = 16, F = 5.409
|
Statistics |
Parramatta Station |
Bankstown Station |
Gosford Station |
Overall |
|
Sample Size |
5 |
5 |
6 |
16 |
|
Mean |
825.8 |
153.2 |
40.0 |
320.9 |
|
Standard Deviation |
748.3 |
79.4 |
29.3 |
526.5 |
The results of the ANOVA table is shown below:
|
df |
SS |
MS |
F |
|
|
Groups |
2 |
1888665.3 |
944332.7 |
5.409 |
|
Error |
13 |
2269435.6 |
174572.0 |
|
|
Total |
15 |
4158100.9 |
According to the above results, the value of the F- test statistic is 5.409.
Now calculate the P-Value using the “Theoretical distribution F”, the P-value graph is shown below:
The P-value corresponding to numerator degree of freedom 2 and denominator degree of freedom 13 is 0.020. Now compare the P-value with 5% level of significance. The P-value 0.020 is less than 5% level of significance, so the null hypothesis of the test gets rejected.
Hence, the means for the three stations is different corresponding to the tap on and tap off.
According to the results obtained in part (a) and Part (b), the Parramatta station have mostly used, so NSW government can build underground railway station from Parramatta station to central.
The dataset covers 40 values, the variable mode has divided into four categories (Bus, Train, Ferry and Light Rail), so it is a nominal level variable. The variable tap specifies the tap type which has divided into 2 categories (on and off), so it is a nominal level variable. The variable gender specifies the type of gender which has divided into 2 categories (male or female), so it is a nominal level variable. The collected data has been provided in the excel spread sheet, the numerical summary is shown below:
|
Count of Mode |
Column Labels |
||
|
Row Labels |
F |
M |
Grand Total |
|
Bus |
5 |
8 |
13 |
|
Ferry |
2 |
3 |
5 |
|
Light rail |
3 |
2 |
5 |
|
Train |
12 |
5 |
17 |
|
Grand Total |
22 |
18 |
40 |
The graphical summary of the gender corresponding to the mode is shown below:
According to the above graph, female tap bus 5 times, ferry 2 times, light rail 3 times and train 12 times while male tap bus 8 times, ferry 3times, lightrail 2 times and train 5 times. Overall, bus was tap 13 times, ferry was 5 times, lightrail was 5 times and train was 17 times. Hence, it can say that, female prefer train transport than male and male prefers bus than female.
Section 5: Discussion & Conclusion
According to the above numerical summary, out of 1000 times, buses was used 463 times, trains was used 503 times, ferry was used 19 times and lightrail was used 15. The people mostly prefer the train (50.30%) and the bus (46.30%) for the public transport. Thus, train was most used by the NSW people during 8th to 14th of August 2016.
There are 50% of public transport users in NSW use the train mode of transport.
The Parramatta station have mostly tapped on/off. The average number of tap on/off is 825.8 and total count of tap on/off are 4129. Parramatta station have mostly used, so government can build underground railway station from Parramatta station to central. Also, NSW government can build underground railway station from Parramatta station to central.
The means for the three stations is different corresponding to the tap on and tap of
References:
Goodwin, S. (2012) SAGE secondary data analysis. India: SAGE publications Pvt. Ltd.
Morgan, D. (2013) Integrating Qualitative and Quantitative methods: A Pragmatic Approach. India: SAGE publications Pvt. Ltd.
Maxwell, R. and Riccardo, R. (2014). A Student’s Guide to Analysis of Variance. Routledge.
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