A Statistician Investigating the Relationship Between the Amount of Precipitation

question 177

Essay

A statistician investigating the relationship between the amount of precipitation (in inches) and the number of car accidents gathered data for 10 randomly selected days. The results are presented below. $$\begin{array} { | c | c | c | } \hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \\\hline 1 & 0.05 & 5 \\\hline 2 & 0.12 & 6 \\\hline 3 & 0.05 & 2 \\\hline 4 & 0.08 & 4 \\\hline 5 & 0.10 & 8 \\\hline 6 & 0.35 & 14 \\\hline 7 & 0.15 & 7 \\\hline 8 & 0.30 & 13 \\\hline 9 & 0.10 & 7 \\\hline 10 & 0.20 & 10 \\\hline\end{array}$$ Calculate the Spearman rank correlation coefficient, and test to determine at the 5% significance level whether we can infer that a linear relationship exists between the number of accidents and the amount of precipitation.

---

Definitions:

Minimum Points

The lowest scores or levels that must be achieved in a particular framework, often used in educational or competitive contexts.

Maximum Points

Refers to the highest value or peak point that can be achieved within a given set of parameters or conditions.

Total Economic Profit

The sum of accounting profit and economic profit, which measures the total earnings of a company after accounting for both explicit and implicit costs.

Profitable Level

The point at which the revenue from sales exceeds the costs involved in production or procurement.