Section 2: Single Variable Analysis in Dataset 1

The manner in which individuals travel to their places of work and learning institutions influences their physic activity level. Due to this, surveys are carried out to assist in planning of physical activity and model travel promotions in institutions and other places in Australia that require travelling (Rissel, Mulley and Ding, 2013). This paper is there aimed at analysing statistical data to determine the commonly used mode of transport and provide recommendations on areas where improvements or new developments should be made.

Datasets

Dataset is a secondary data since it is collected from a secondary source; Australian website for transport and is a subset of the data “Opal Tap on and Tap off location- 8^th to 14^th August 2016” provided by the transport for NSW Open data (Opendata.transport.nsw.gov.au, 2016). It has got five variables; mode, tap, loc and count. Mode is a categorical variable with cases; bus, train, ferry and light trail indicating the type of public transport used. Tap is a categorical variable with cases; on and off indicating whether it’s a tap on or a tap off. Loc is a categorical variable with cases; train stations and postal codes. Count is a numerical variable indicating the count of the mode of transport. Date is a quantitative continuous variable indicating when the tape was held (Bruce, 2015).

Dataset 2 is primary data is collected from a one-on-one survey for 160 individuals (Fowler, 2009). This dataset has three variables, date is quantitative continuous variable indicating the date when it was collected, gender is a categorical variable with two case; male of female indicating the sex of the person interviewed. Mode is categorical variable with cases indicating mode of transport used (Bruce, 2015).

Section 2

Single Variable Analysis in Dataset 1

The means of transport that was commonly used by the NSW people between the dates 8^th to 14^th August, 2016 is determined using sum of total and proportion of total as the summary statistics. The sum of total represents the total sum of count of a given mode of transport while proportion represents the sum of count for a given mode of transport as a fraction of the total. The table of the summary statistics is as shown below:

Summary Stat

It is clear that buses were commonly used mode of transport, followed by train, then ferry and lastly light trail. The above summary statistics are visualized using a pie chart. A pie chart is a method of data representation that uses a circle that is divided to portions equivalent to proportions being represented (Rumsey, 2007). In this case the proportion is the mode of transport as a percentage of the total. It is as shown below:

To prove whether more than 50% of the population used the mode with the highest proportion as their preferred mode of transport, a hypothesis is formulated and tested. Our sample size is 1000 and the highest proportion for the mode of transport (buses) was 0.48. To process of formulation and testing of the hypothesis follows the steps below:

Section 3: Two Variable Analysis in Dataset 1

Step 1: The initial step is to state the null and alternate hypothesis.

Step 2: Check whether all the conditions for the hypothesis are met

All the conditions are met

Step 3: Determine the Z-test statistic.

Step 4: Developing a decision rule.

Using the default significance level of 0.05 the decision rule will be to accept the null hypothesis when the P-value for the z-statistic P(Z>-1.26) =0.104 is within the range of -1.96 to 1.96 (Lock et al., 2013). Since the p value is within the required range, we accept the null hypothesis and conclude that more than 50% of the population used the mode with highest proportion as their preferred mode of transport with the specified period.

Section 3

Two Variable Analysis in Dataset 1

To prepare the recommendation on which substation the government should build the underground railway from to central, the data is filtered with train as the mode of transport, the three stations required for consideration and count. The data is filtered in excel using the filter function (Linoff, 2008). Once the data is filtered for the required variables the online stat-key statistic tool is used for analysis(Lock5stat.com, 2018). The summary statistics for the filtered data is as shown below:

Summary Statistics 2

The data above is visualized with the aid of the box plot shown below. A box plot visualizes data in terms of the median indicating also the direction of skewness for the data.

From the summary statistics and the box plot it is evident that Parramatta station offers the greatest of service compared to the rest of the stations therefore it would be okay to recommend to the NSW government to construct the underground station from the Parramatta station to central to ease the services in the station.

To discern whether there is a difference in the mean for count and taps, hypothesis at 5% significance level is carried out in stat-key software. The null hypothesis in this case is that there is no difference between means while the alternate hypothesis is that there is a difference between means. The first step involves determining the sample sizes and the means. The result for the means is as shown below:

Sample means and sizes

From the above table, the sample sizes are both greater than 30 and the standard deviation for a given sample is not twice as much as the other hence all the conditions for the hypothesis test are met.

Step 2 involves determining the degrees of freedom of the numerator and denominator using the ANOVA table. The results for the degrees of freedom is as shown below:

Degrees of Freedom

The degree of freedom for the numerator is 1 while that of the denominator is 998.

In step three a graph of F distribution that will also indicate the p value is drawn and is as shown below:

The P-value determined is 0.025 and since its less than the significance level we cannot accept the null hypothesis. This means that there is a difference in the means for tap on and tap off.

Section 4

Analysis of Dataset 2

The dataset is collect from a one-on-one interview of potential individuals. It has got three variables namely; date, gender and mode. Date is when the survey was taken, gender is the sex of the person interviewed and mode is the preferred mode of transport by the interviewed person. Summary statistics are developed to indicated what mode of transport is most preferred and by which gender. The table for the summary statistics is shown below:

Summary Statistics 3

The data is visualized with the aid of a stacked bar chart. A stacked bar chart is similar to the normal bar chart only that it is used for two categorical variables.

From the stacked bat chart and the summary statistics, it’s clear that most people prefer buses to other modes of transport, followed by train, ferry and last in the list is light trail. Most male prefer bus to women, same case with the train. However, for the ferry and light rail the contrary is the truth.

Section 5

Conclusion

The data analysis performed indicate that most people prefer buses and train for transport. This can be attributed to the services offered by the various stations of the buses and the train, ease of access, flexible services and reduced cost. On the other hand, it is clear that Parramatta train station offers most of the services hence the NSW government should build the underground railway to central form this station. Future research should be conducted to examine what factors attract customers to their preferred mode of transport and the patterns in which the various modes of transport are used so that the government can set priorities during planning, modelling and development.

References

Bruce, P. (2015). Introductory statistics and analytics. New Jersey: Wiley.

Fowler, F. (2009). Survey research methods. 4^th ed. London: Sage Publication.

Linoff, G. (2008). Data analysis using SQL and Excel. Indianapolis, Ind.: Wiley Pub.

Lock, R., Lock, P., Morgan, K., Lock, E. and Lock, D. (2013). Statistics: Unlocking the power of data. Wiley.

Lock5stat.com. (2018). Theoretical distribution. [online] Available at: https://www.lock5stat.com/StatKey/theoretical_distribution/theoretical_distribution.html#normal [Accessed 21 Sep. 2018].

Opendata.transport.nsw.gov.au. (2016). Opal Tap On and Tap Off | TfNSW Open Data Hub and Developer Portal. [online] Available at: https://opendata.transport.nsw.gov.au/dataset/opal-tap-on-and-tap-off [Accessed 21 Sep. 2018].

Rissel, C., Mulley, C. and Ding, D. (2013). Travel mode and physical activity at Sydney University. International Journal of Environmental Research and Public Health, [online] 10(8). Available at: https://www.mdpi.com/1660-4601/10/8/3563/pdf [Accessed 21 Sep. 2018].

Rumsey, D. (2007). Intermediate statistics for dummies. 1^st ed. Hoboken, N.J.: Wiley.