Level 2 2.9 stats PDF

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Please use this document to type your Formative Report for 2.9 Statistical Inference Please enter your name, form and teacher code in the header above. Please type your investigative question here: -

Is the median selling price (in dollars) for houses in zone 8 higher than the median selling price (in dollars) for houses in zone 5 in the 2016 NShorehouse dataset?

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The reason I think houses in zone 8 will cost more than houses in zone 5, because houses in zone 8 have a better location close enough to Auckland city, and is only a ferry ride away from Auckland's CBD so transport is very easy. Also houses in zone 8 have beautiful seaside views of Rangitoto island, and often houses in zone 8 are quite big and spacious compared to houses in zone 5. Houses in zone 5 cost a lot cheaper because it is an industrial area, and houses are quite small compared to houses in zone 8 and are a lot older as well.

Please take your samples and insert your complete NZGrapher output here;

Please write your INFERENCE statements here, and answer your investigative question: Confidence interval for zone 5 :(691,356 - 766,284) Confidence interval for zone 8: (1,124,902 - 1,588,276) Interpreting the meaning for the CI for zone 5: The confidence interval for the house selling price for houses in zone 5 suggests that back in the population of the 2016 NShorehouse data set, that the median selling price for houses in zone 5 is likely to be somewhere between $691,356 -$766,284.  CI for Zone 8: The confidence interval for the house selling price for houses in zone 8 suggests that back in the population of the 2016 NShorehouse data set, that the median selling price for houses in zone 5 is likely to be somewhere between $1,124,902 - $1,588,276. I nference Since there is no overlap whatsoever between these confidence intervals of selling prices in zone 5 and zone 8, I have sufficient evidence to make the claim that the median selling price for houses in

zone 8, back in the population of the 2016 NShorehouse data set, is more than median selling prices for the houses in zone 5. Discuss sampling variability: The gap between the upper limit of the selling price for houses in zone 5 confidence interval and the lower limit of the selling price for houses in zone 8 is very large being $358,618. If I were to repeat the sampling process with the same sample size, although I will get slightly different results due to sample to sample variability, it is very highly unlikely that the confidence intervals will overlap. Therefore I would expect to come to the same conclusion that the median selling price for houses in zone 8 is a lot higher than the median selling price for houses in zone 5. Now complete the rest of your investigation by comparing the features of the sample distributions and discussing sampling variability, including the variability of estimates. Sampling method: I have used simple random sampling to select these two samples of selling price for 2 different house zones because simple random sampling is likely to give me representative samples with regard to those factors which may affect the price of a house, other than its zone. For example, houses in zone 8 (devenport, stanley point) cost more than houses in zone 5 (glenfield and wairau park) because they are usually bigger and have better views (of rangitoto island),I therefore need samples which have about the same proportion of houses in zone 5 and houses in zone 8 as there are in this population. Random sampling is likely to produce that. Sampling size: I have selected samples of size 30 as, in a classroom activity, I found that a sample of size 30 optimised the degree of sample to sample variation in the sample medians. It kept this variation small enough to likely give an accurate estimate of the population median without being an overly large sample that can cost or take a lot of time. A small sample (e.g. n=10) would have too much sample to sample variation in the sample medians to produce a reliable estimates of the population median house selling prices for zone 5 and zone 8.

Centre: The median line (selling price) for the houses in zone 8 falls to the extreme right of the median line for selling prices for the houses in zone 5. This indicates that the median selling price for houses in zone 8 are a lot more expensive than median selling price for houses in zone 5. This is confirmed by the statistics provided, where the median house selling price for houses in zone 8 is $1,356,588, while the median selling price for houses in zone 5 is only $722,828 which is $633,760 less than the median selling price for houses in zone 8. The sample mean selling prices also confirm that, the mean price for zone 8 being $1,677,300 and the mean prices for houses in zone 5 being $740,180. The mean price is slightly higher than the median price because of the highly expensive house ($5,850,000) which was included when calculating the mean but not the median. Both of these statistics are in line with my hypothesis, that houses in zone 8 cost on average more than houses in zone 5.

Spread: Visually, in the boxplots above, the box for the selling prices in zone 8 sample is a lot longer than the box for the selling prices in zone 5 sample (almost 8 times longer). This shows that there is more variation in the middle 50% of the sample of selling prices in zone 8 than the middle 50% of the sample of selling prices in zone 5. This is confirmed by the IQR ranges, where the IQR for the sample of selling prices in zone 8 is $846,000 while the IQR for the sample of selling prices in houses in zone 5 is only $136,800, which is 6 times less than the IQR for the sample of selling prices in zone 8. Shift and overlap: The box of the selling prices in zone 8 is shifted further up the scale to the right of the box of the selling prices in zone 5, which is in line with my hypothesis that houses in zone 8 cost more than houses in zone 5. There is no overlap of the box at all, which shows how the prices of houses in the 2 zones are completely different and there is no similarity between the selling prices of houses in the 2 zones, which again confirms my hypothesis. Shape and Unusual features: The distribution of the selling prices for zone 5 is bell-shaped and fairly symmetrical. .These are concentrated in the low values with a mode at around $700000, similar to the median and all lie in a small range between about $500,000 and $800,000. The mode for zone 8 is much higher at about $1.4million, also similar to the median. While the distribution of the selling prices for zone 8 is right-skewed which was expected since houses in zone 8 are a lot more expensive than houses in zone 5. The mode for zone 8 is much higher than the mode for zone 5 at about $1.4 million which is similar to the mean.There is an unusual value of highly expensive house valued at $5,850,000 which could be the price of a mansion or a really big house with multiple bedrooms. There are no unusual values in the sample of the selling prices for houses in zone 5. Now confirm your inference that you have sufficient evidence to claim that the median selling price for all houses in Zone 8 the 2016 NSHD is higher than the median selling price for all houses in zone 5 in the 2016 NSHD....