Achieved:

Context: According to Wikipedia when the titanic sank it only had enough lifeboats to carry about half of those on board and third-class passengers who I think would have paid way less for their fares were largely left to fend for themselves, causing many of them to become trapped below decks as the ship filled with water. In fact “54% of those in third class died”. 

Question: I wonder if there is a difference between the median fares of people that were on the Titanic in 1912, who survived and who did not, according to a sample provided from a Titanic passenger list. I am doing this investigation to discover whether the more money you payed increased a passenger's chances of survival. 

Hypothesis: I think that if you were in first class on the Titanic, it would have increased your chances of survival because in Wikipedia it says that the first class passengers were closer to the lifeboats. 

Merit:

Question: I wonder what is the difference ls between the median fare of the Titanic passengers of those who survived and those who unfortunately didn't survive the horrific Titanic accident in 1912. 

Context: My research shows that the median fare price that was paid by the survivors was higher than the median fare price that was paid by non-survivors. For example, my research states that a first class ticket today costs around £83200 today and the third class tickets cost around £298-£793. Of the first class riders, 60% of them had all survived. I also discovered that first-class facilities and accommodation was located on the top decks of the Titanic to avoid the vibrations and noise of the engines which were at the bottom of the ship. This also meant that first class passengers were closer to the lifeboats. Only 25% of the third class ticket buyers survived, as they were closer to the bottom of the boat and because of this they were further from the lifeboats. Also, the Titanic itself was built to gold 32 lifeboats, however, only 20 were on board at the time. One of the lifeboats had the capacity to hold 65 people, however, only 27 carried on the lifeboat, so I feel that there should have been more lifeboats on board for caution. In total there was 2228 people on board the Titanic, but only 705 survived and 1523 unfortunately perished. Using this research and data, I will be able to conclude whether or not it is statistically true that those who paid a higher price were more likely to survive. 

Hypothesis: My prediction is that the median price a person who survived paid for a ticket will be higher. The fare is the price that passengers of the Titanic paid to board the ship in British pounds. 

Excellence:

Context: House prices vary between New Zealand's cities and towns . If a teacher is moving to New Zealand from overseas and having to choose where to take a position out of the four main centres of Wellington, Auckland, Dunedin and Christchurch from overseas house prices may influence their final choice of destination, especially if they have limited funds available to purchase a house. Having the right information available will help them to choose a centre where they can afford a house, and this will make it more possible for them to feel at home in New Zealand and not feel financial pressure. This report investigates whether there is a difference in North Island house prices compared to South Island house prices for median house sales price (NZD) in Auckland, Wellington, Christchurch and Dunedin in 2016 to help teachers choose where in New Zealand they may want to look at purchasing a house. Thus, the variables for this investigation are location by island (categorical) and 2016 house sale price (NZD). This data has come from the Real Estate Institute of New Zealand. 

Question: What is the difference between the median house sales price (NZD) in Auckland, Wellington, Christchurch and Dunedin in 2016 for North Island median sales price compared to South Island median sales price? 

Hypothesis: Given that, North Island prices are higher than South Island prices, and Auckland prices are higher than prices in other cities and the Auckland housing market is so ‘hot’, it is expected this report will show the median house sales price (NZD) in Auckland, Wellington, Christchurch and Dunedin in 2016 will have a higher median sale price for North Island properties than South Island properties 

Excellence:

The shape distribution of weekly rental cost (NZD) of North Island properties in New Zealand appears to be right-skewed. This is because there is a longer tail on the right side of the distribution. Outliers are also visible on the far right of the main cluster of data points, around the $4500 range. This indicates a few properties with significantly higher weekly rental costs in the North Island. This may be due to property size, market demands, amenities, etc. Meanwhile, the shape distribution of weekly rental cost (NZD) of South Island properties in New Zealand also appears to be symmetrical. This is because the two sides of the distribution are a mirror image of each other. It has one peak and a bell-curved shape. There are no visible outliers. In context, this suggests that the weekly rental costs are relatively consistent across different properties on South Island. This might be because the features of the properties of South Island have similar characteristics, such as the size or quality of the construction. This similar nature can lead to more uniform, stable and predictable rental market prices. 

The distribution for North Island is skewed right. Therefore, it’s an asymmetrical distribution. While the distribution for the South Island is symmetrical. Considering both of these features, I will be using the median as the measure of the centre. My reason for this is that the North Island distribution contains extreme outliers; therefore, if I use mean as my measure of centre, it will be heavily impacted by extreme values and outliers. Hence, using the median to measure the centre will provide a better representation, as it avoids distortion from extreme values. As for the distribution for the South Island is symmetrical; therefore, either mean or median can be used interchangeably. For these same reasons, I will be using the Interquartile Range (IQR) as my measure of spread because using IQR helps mitigate the influence of these outliers in the North Island distribution. While the South Island’s distribution is symmetrical, using the IQR provides a consistent measure of spread that can be compared directly to the North Island’s IQR.

 The median weekly rental cost (NZD) of North Island is $750. Meanwhile, South Island's median weekly rental cost (NZD) is $570. This suggests that in my sample, the North Island median weekly rental cost is higher than the South Island median weekly rental cost by $180 on average. This further supports my research and prior research, highlighting the difference in regional rental costs between the North and South Islands of New Zealand. Once again, one major factor leading to this difference may be that North Island is home to larger cities like Auckland and Wellington, increasing demand for rental properties and driving up rental prices. According to a source, NZ Herald talks about house prices rising due to migration and demand for new-build homes, stating, “In an environment of strong population growth, this decline in new house supply can do only one thing to prices – push them higher.” This suggests that the surge in migration, both international and domestic, is significantly influencing rental prices and has intensified the competition for available rental properties, thus driving up prices.

North Island IQR
$950 - $580 = $370

South Island IQR
$640 - $485 = $155

The interquartile range of my sample of weekly rental cost (NZD) of North Island is $370. Meanwhile, the interquartile range of my sample of weekly rental costs (NZD) for South Island is $155. This means the middle 50% of both Islands show considerably wide rental cost variability. This may be due to economic conditions and urbanisation. The South Island’s lower IQR of $155 suggests that rental prices are clustered more closely around the median, showing less variability and more uniform stable rental prices. Meanwhile, North Island’s higher IQR of $370 suggests a broader spread of rental costs, thus resulting in greater variability and less stability in rental prices.

Within my sample of the North Island’s weekly rental cost (NZD), I can identify eight clear outliers. These outliers, ranging from $2000 to $4500 per week, are particularly intriguing. They may be due to different types of luxurious properties, ranging from high-end apartments to penthouses. The greatest outlier for North Island weekly rentals is NZD $4500, hinting at the possibility of a luxurious property, often located in prime urban or waterfront locations. Meanwhile, within my sample of South Island’s weekly rental cost (NZD), I can identify three outliers in the $1000 range. Although closely clustered around the upper quartile, they still qualify as outliers since they lie beyond 1.5 times the interquartile range above the upper quartile. A possible explanation is probably because of unique accommodations and properties with exclusive access to natural attractions, which drive up the rental prices.

High Merit:
The median of the survivors is £14.37 higher than the median of the non survivors, as it is £26.55 compared to the non-survivors £12.18. I am looking at the median rather than the mean because the extreme values affect what the center looks like, therefore the mean isn't used. So far this is lining up with my expectations as I expect that the people who paid a higher fare rate more likely survived. This supports my research because it showed that those who paid more were able to allow them to stay on one of the higher decks of the ship, therefore increasing their chances of survival as they were further away from the danger. For example, of the third class survivors, only 25% of the people that stayed on that level survived. Whereas the percentage of people that survived that stayed in first class was 60%. 

The middle 50% of the non-survivors fares are between £8 and £26, whereas the middle 50% of the survivors fares are between £13.70 and £52.80 Saying this, there is quite a bit of overlap between the upper quartile of the non-survivors and the lower quartile of the survivors. So this suggests that there was quite a difference in the fares paid and that survivors on the Titanic in 1912 paid more for their ticket than the non-survivors. This once again can be linked to my research as this result lined up with my expectations, as I had predicted that those who survived paid a higher median fare price. This is because if they paid more, they would have been staying in one of the rooms on the upper deck. 

The interquartile range for the survivors is £39.10 whereas the interquartile range for the non-survivors is £18, indicating that the survivors have more variation in the fare price that they had paid than the non-survivors. The standard deviation is also higher for the survivors. Overall, visually the survivors seem to be slightly more spread out than the non-survivors. The shapes of both graphs are different when compared to each other. The non-survivors fare paid seems to be a bimodal graph with a peak close to around £7-8 and another peak near £25. 

On the other hand the survivors fare paid seems to be a unimodal graph with a mode around the median of £26.55. Although it is very skewed to the right it has a shorter tail stretching from the upper quartile to the highest value than the non- survivors graph. This supports my prediction because on the survivors data there is more people that paid more for their fare, which is why they were more likely to survive. 

Making the Call:
We can be reasonably confident that for these populations of people currently renting in the North and South Islands of New Zealand, the mean rent per week will be between $221.80 to $578.46 more expensive in the North Island than the South Island. As zero isn’t included in this bootstrapped confidence interval and there is enough evidence to make a call, that there is a difference between the mean rent per week price between rent in the North and South Island.

Connection to Hypothesis
This conclusion supports our hypothesis that people who rent a property in the South Island tend to have a cheaper median/mean weekly rent price (in $NZD) compared to those in the North Island. This is reinforced by our investigational data, including the results from our bootstrapping analysis, which provides strong evidence for the observed difference in rental prices between the two islands. 

Sampling Variability:
If I took another sample, I would get different mean rent per week prices as I would be collecting data from different renters in the North and South Islands of New Zealand. I would expect my summary statistics to be (minimum, LQ, mean, UQ, maximum) to be similar, but not the same as my current investigational results. Because the mean rent per week price of North and South Island rent would be similar, this would lead to a similar bootstrap confidence interval, and therefore the conclusion that rent per week prices are higher in the North Island than in the South Island is likely to remain the same.

Mean vs Median:
I decided to select mean as my parameter for my investigation. This is because when removing outliers from the box and whisker graphs of both the North and South Island rent, the distributions of both were relatively normal and neither graph had any extreme values, meaning my results wouldn’t be greatly affected. If I were to use median instead we would get values of $700 per week for North Island and $565 per week for the South Island. These values are similar and different to the means, as the North Island mean for rent per week was $948.81, very different from the median. The South Island mean for rent per week was $571.92, which was very similar to the median. In the North Island, there is a big difference between the rent per week price between mean and median. This could be because there are more outliers present, and the outliers can have a greater effect on the mean, a reason as to why it is is greater that the median. In the South, the difference between mean and median for rent price per week is much smaller/they are more similar, this could be due to there being very little to none extreme outliers, meaning there is little to no effect on the mean.

Sample Size and Sampling Error
If I were to use a smaller sample for my investigation, it would result in larger sampling error. A larger sampling error would mean that there would be a larger confidence interval on my bootstrapped graph. Bootstrapping is the process of resampling a dataset multiple times, and in the case of my experiment I resampled my data 1000 times. Each resample has a different mean to the next or last, and the difference between these means (DBM) is plotted to create the bootstrapped confidence interval. There are a number of factors that could affect the mean rent per week price of rental properties in the North and South Islands of New Zealand. One factor is that my sample size was a small  sample. To help widen the data and show a greater amount of rental prices, a larger sample size would be required, such as 500 rental properties per group. My sample is not representative of all rental properties in the North and South Islands of New Zealand. Another factor that could affect the mean rental price per week is the after-effects of the rent freeze that happened in New Zealand during the beginning of the COVID-19 pandemic. After this rent freeze ended in September of 2020, the mean prices of rent nationwide went from $450 to $501 in December 2020. In my research, I can see that this increase of rent has continued, showing the after-effects of COVID-19 are still not over.

Next Steps
I believe that further research is required to see whether subsidies or different living situation options are required to alleviate the struggles people that rent a property are experiencing due to the cost of living crisis, as mentioned in my purpose. The governmental agencies like the Ministry of Housing and Development, Ministry of Social Development and Tenancy Services (falls under Ministry of Business, Innovation and Employment) could contact all of the people who are currently renting a residential property in New Zealand and conduct a survey similar to the NZ Census and find out how people are struggling to afford in order to maintain a good quality of life. This way, the various ministries can figure out strategies of how to help people who cannot afford rent along with bills and food. The ministries can calculate how they can provide support to those who need it, or remake the benefits strategy to include more groups of people and turn it towards helping rent decrease. Potentially, they could create a similar rent freeze as they did in 2020, but not complete freeze rents, but help them stay at similar levels for longer.