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###### BUS708 Statistics And Business Data Analysis

##### Question:

**Section 1: Introduction**

Give a brief introduction about the assignment and search-related Article and write a one-paragraph of summary which should be a support for your assignment. You need to give the full citation of the article.

**Dataset 1:** Give a short description of this dataset. Is this primary or secondary data? What are the types of variables involved? Explain briefly what are the possible cases used in this study.

**Dataset 2:** Explain how you collect the data and discuss its limitation (e.g. whether your sample is biased). Is this primary or secondary data? What is/are the type(s) of variable(s) involved? Give a description of cases you consider for this data set.

**Section 2: Analysis of single variable in Dataset 1**To answer the research question “What is the shape of the distribution of the variable All Flights?”, provide a suitable numerical summary and graphical display for the variables All Flight of Dataset 1. Give detailed comments to answer the research question.

Now to answer the research question “Is the average number of flights came in and flew out to Australia in a month between September 2003 and September 2018 more than 30?” setup an appropriate hypothesis, perform hypotheses test by checking all the assumptions and answer the research question by writing the conclusion of the test.

##### Answer:

#### Introduction

**a)** The significance of this report needs to analysed in the given context where in Australia, there is increased international traffic. Further, another interesting development is that there is a rising market share of international airlines with regards to international travel originating or ending in Australia. The market share growth rate comparison for domestic and international players tends to provide testimony to the above statement. A contributing factor to the higher growth rate of international carriers may be attributed to capacity cutting by Qantas as an efficiency measure for improving occupancy (Anna Aero, 2018). For capturing this increasing market, it is imperative that the Australian airports need to understand the preferences and needs of the consumers and make suitable adjustments.

**b)**Dataset 1 highlights the information of the sample of 1000 international flights that have any Australian city as the source or the destination. This dataset has several variables pertaining to these flights related to information regarding source, destination, route, frequency of given flight in a month, stops count and maximum seats available. This data of 1000 flights would be considered as secondary data as this data is not collected myself but has been obtained from an external source by the University. While the dataset has a host of variables, a significant amount of these are non-numerical variables which are labelled as categorical variables. These are represented in the dataset with the use of nominal measurement scale. But some variables are there in the dataset which have numerical values and are thus not categorical which have used ratio scale for measurement (Hastie, Tibshirani and Friedman, 2014). The typical cases for the dataset would be driven by the underlying population which essentially constitutes of every international flight during the given period flying from or to Australia.**c)**Dataset 2 comprises of primary data which is different from dataset 1. This data is termed as primary as the underlying data represented has been collected through conducted survey by myself and the underlying data has not been copied from any other source. The respondents (35 in total) for the requisite survey were KOI students. Unlike dataset 1, this dataset 2 offers scope that is les wider as instead of multiple variables expressed in dataset 1, just three variables are included here i.e. city in Australia, Airline and city abroad. For the given variables, the underlying data measurement technique is nominal considering categorical data that cannot be automatically arranged in any order. The reliability of the conclusions based on the given data may be adversely impacted on account of use of non-probability sampling technique where instead of choosing KOI students randomly these were chosen driven by own convenience. This may have led to the sample being bias thereby impacting the overall reliability (Fehr and Grossman, 2013).

- The summary statistics for the variable “All Flight” have been computed using Excel and highlighted as follows.

With regards to shape, one of the most crucial parameters is the skew which is positive and quite high in value. This implies that while majority of data points would be represented at the lower end but there would exist some data points which are eexceptionally large and would lead to a lengthy tail on the right of the mean. This conclusion is supported from the fact that the mean is 24.56, the maximum value is 162 which clearly imply that outliers may be present in the data on the higher side. However, this high range is on expected lines owing to traffic demand varying significantly on different sectors because of which the number of flights operating on the sector would also vary. Hence, the underlying shape of the distribution of “All Flight” would be asymmetric owing to presence of a large skew.

THe “All Flights” variable data can be summarised using a histogram as represented below.

It is apparent from above that more than 50% of the flights have monthly frequency now exceeding 25. Additionally about 360 flights have a monthly frequency not exceeding 50. The net result is that 85% of the sample international flights have monthly frequency that fails to cross 50. However, there are certain international flights which are high in demand owing to which the monthly frequency is very high and also exceeds 150. This has led to an asymmetric shape of distribution with a long rightward tail thereby highlighting the non-normal distribution of the given variable.

- A hypothesis test would be the requisite tool of choice for the problem as hand as this technique allows testing of claims for the population of interest using sample data at hand (Harmon, 2016). This process begins with the defining of the hypotheses as has been carried out below.

The significance level determines the results precision for the hypothesis test and this has been taken as 5% in the given case.

The appropriate test statistic needs to be defined so that relevant testing can be performed. Considering the situation at hand, this test statistic would be t since the population standard deviation has not been provided. Also, the alternate hypothesis indicates that the relevant test is a single tail (left tail) test (Koch, 2016). The execution of the hypothesis test has been carried out in Excel and the obtained output is illustrated below.

The critical output data that is relevant to decide on the rejection of null hypothesis is the p value. This has been derived as 0.000. The underlying decision rule states that null hypothesis would be rejected only when the significance level is not lower than the p value. Also, when the null hypothesis is rejected, it would imply that the alternate hypothesis is accepted (Lehman and Romano, 2016).

In the given hypothesis test, the p value is lower than significance level and hence null hypothesis is rejected and alternate hypothesis is accepted. As a result, the conclusion is that international flights coming and leaving Australia in a month do not exceed on average 30 for the relevant time period.

- a) Taking the provided sample data into consideration, the distribution with regards to specific Australian airports (ie. Brisbane, Sydney & Melbourne) along with specific airlines (Singapore Airlines, Cathay Pacific & Air New Zealand) needs to be summarised. The summary of the above in numerical terms is presented as follows.

The above numerical summary can also be depicted graphically as highlighted below.

In terms of airport, the summary measures above outline that maximum flights from the selected airlines tend to use Melbourne since more than 40% sample flights either originate from Melbourne or end at Melbourne. After Melbourne, the next highest traffic from the three outlined airlines is accounted for by Sydney which has 25 flights as compared to 36 flights for Melbourne. Last is Brisbane with only 18 flights. Additionally, it can be seen that variation in the usage of different airports can be seen by the three outlined airlines. For instance, in context of Singapore Airlines, maximum flights are received at Melbourne and minimum at Sydney. But this is not the same for Cathay Pacific where Melbourne has the maximum flights but minimum flights are with Sydney and not Brisbane. Additionally, it can be seen that there is a significant difference in the number of flights from the three different airlines included in the sample. A significant chunk belongs to Air New Zealand which should not raise an eye brow as New Zealand and Australia are geographically quite close owing to which the amount of traffic is also significantly higher between the two countries as compared to the flights from other far flung nations.

- A hypothesis test would be the requisite tool of choice for the problem as hand as this technique allows testing of claims for the population of interest using sample data at hand. This process begins with the defining of the hypotheses as has been carried out below.

The significance level determines the results precision for the hypothesis test and this has been taken as 5% in the given case.

A key observation for the variables at hand is that these are categorical and non-numerical. This implies that the test of choice for these would be Chi-square test of independence (Koch, 2016). This hypothesis test has been performed with the aid of Excel and relevant output pasted as follows.

The critical output data that is relevant to decide on the rejection of null hypothesis is the p value. This has been derived as 0.000. The underlying decision rule states that null hypothesis would be rejected only when the significance level is not lower than the p value. Also, when the null hypothesis is rejected, it would imply that the alternate hypothesis is accepted (Harmon, 2013).

The computed p value from the output above is 0.3170 which exceeds the significance level for the hypothesis test. This would imply availability of insufficient evidence to warrant null hypothesis rejection. Hence, alternate hypothesis cannot be accepted. Therefore, it is appropriate to conclude that level of association between selected Australian airports and the selected airlines is not found to be statistically significant.

- c) As the relation between the Australian airports and respective international airlines is not statistically significant, therefore the comparison of performance of the airports should be carried based on the sample data and the amount of traffic from these airports. Taking this into consideration, the best performer would be Melbourne (36), followed by Sydney (25) and Brisbane occupying the last position with 18 flights only.

The graphical representation of the responses derived from 35 students enrolled in KOI is summarised as follows.

The above survey summary highlights that maximum number of international flights tend to be linked to Melbourne (16) which is closely followed by Sydney (15) while Brisbane languishes at the third position with only 8 flights. The difference between performance of Melbourne and Sydney is only slight and not as significant as was reflected by Dataset 1. A significant difference between the summary of Dataset 1 and Dataset 2 is that the former focused only on three selected airlines which is not the case for Dataset 2. A potential disadvantage of Dataset 2 and the results highlighted above is that they may lack in reliability as the sample was not selected through random sampling. Also, it may be possible that preferences of KOI students may differ from the other set of users that formed the basis of Dataset 1.

Based on the analysis of the flight variable, it has come to light that the distribution is asymmetric as a high amount of positive skew is present in the sample data. This may be attributed to differing demand of passengers on different routes and hence different frequencies of flights on different routes. For the time period under consideration, it has been concluded that average monthly flight from or to Australia does not exceed 30. Considering the selected airports in Australia and selected airlines, the hypothesis test do not highlight any significant association which implies there is no preference on the part of the airlines for any particular airport city. The airport performance hence has been judged based on the sample data as per which Melbourne hosts the maximum traffic in the sample data from the selected airlines while Brisbane has the least. The reasons for these differences need to be analysed so that prudent recommendations on improving services can be offered. With regards to Dataset 2, a similar pattern in terms of traffic has been seen as in Dataset 1 with the difference being that dataset 1 was limited to just three airlines which is not the case with dataset 2.

In regards to research going forward, it makes sense that the researcher ought to study specific groups so as to understand the precise parameters that tend to drive their choices of airport that they choose as their source and destination. This would be vital in airports providing better services to customers and also in understanding if the preferences of specific group differ from one another.

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