As A Result Of A Prolonged Economic Boom Toronto Is Undergoi

1as A Result Of A Prolonged Economic Boom Toronto Is Undergoing Se

As a result of a prolonged economic boom, Toronto is experiencing various social and economic changes, notably the housing affordability crisis among young people. The problem revolves around analyzing the trend in median house prices over a 12-month period, calculating relevant statistical measures, and determining whether the median price has increased beyond an established affordability threshold of $195,000. The analysis involves graphing the data, computing the mean and standard deviation, finding the range and mode, and applying hypothesis testing at a 5% significance level to assess the change in median house prices over time.

Paper For Above instruction

Toronto’s ongoing economic prosperity has significantly impacted its housing market, especially concerning the affordability for young residents. The provided data records median house prices from January to December, revealing a fluctuating but generally upward tendency. This paper delves into analyzing these changes comprehensively by visualizing the data through graphing, calculating key statistical measures, and conducting inferential statistical testing to understand the trend's significance.

Graphing and Describing the Data Trend

Beginning with visual analysis, plotting the median house prices over the months indicates a pattern of gradual increase with some fluctuations. The initial prices in January start at $195,000, and by May, they rise to $212,000, indicating an upward trend. However, the prices fluctuate in the subsequent months, with notable dips in December to $190,000. The overall visual trend suggests a positive slope, representing an increasing median price, but with variability that necessitates statistical analysis for confirmation.

Calculating the Mean and Standard Deviation

The median house prices for the 12 months are: 195, 196, 205, 210, 212, 210, 205, 199, 201, 197, 192, 190. To compute the mean, sum these values and divide by 12:

Mean = (195 + 196 + 205 + 210 + 212 + 210 + 205 + 199 + 201 + 197 + 192 + 190) / 12 = 2,399 / 12 ≈ 199.92 (thousand dollars)

The standard deviation measures the variability of the data. Calculating the squared deviations from the mean and computing the square root of their average yields: approximately 7.17 thousand dollars. This indicates moderate variability around the mean price.

Range and Mode

The range, which is the difference between the maximum and minimum values, is:

Range = 212 - 190 = 22 thousand dollars

The mode, representing the most frequently occurring value, appears to be absent in this dataset as all prices are unique; thus, there is no mode.

Hypothesis Testing: Has the Median Price Increased Beyond the Threshold?

If $195K is considered the threshold for affordability, we want to test at the 5% significance level whether the median house price has increased beyond this threshold during this period. The null hypothesis (H₀) states that the median price is less than or equal to $195,000, and the alternative hypothesis (H₁) states that it is greater than $195,000.

Applying a one-sample t-test with the sample mean of approximately $199,920 and standard deviation of about $7,170, the test statistic (t) is:

t = (sample mean - hypothesized mean) / (standard deviation / √n) = (199.92 - 195) / (7.17 / √12) ≈ 4.92 / 2.07 ≈ 2.38

Consulting t-distribution tables, with 11 degrees of freedom, the critical value for a one-tailed test at α=0.05 is approximately 1.795. Our calculated t-value exceeds this, leading us to reject the null hypothesis, indicating statistically significant evidence that median prices have increased beyond $195,000 in this period.

Conclusion

The statistical analysis supports the conclusion that during the one-year period, Toronto’s median house prices have risen significantly beyond the affordability threshold of $195,000. This aligns with concerns over housing affordability faced by young urban residents. These findings highlight the importance of continuous monitoring and policy interventions to mitigate housing affordability issues amid ongoing economic growth.

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