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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

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[ACTION NAME]

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...

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system
Wearing a helmet is a responsible behavior for both families and society. A certain city continuously educates its residents on safety. The table below shows the statistical data of drivers not wearing helmets captured by surveillance equipment at a main intersection in the city for $4$ consecutive years:

| Year | $2019$ | $2020$ | $2021$ | $2022$ |
|------|--------|--------|--------|--------|
| Year Number $x$ | $1$ | $2$ | $3$ | $4$ |
| Number of People Not Wearing Helmets $y$ | $1250$ | $1050$ | $1000$ | $900$ |

$(1)$ Please use the given data to find the regression line equation $\hat{y}=\hat{b}x+\hat{a}$ between the number of people not wearing helmets $y$ and the year number $x$, and estimate the number of people not wearing helmets in $2023$ at this intersection;<br/>$(2)$ The traffic police recorded $50$ accidents involving electric scooter riders passing through this intersection from $2019$ to $2022$. Analyze the relationship between not wearing helmets and accident casualties, as shown in the table below. Can we be $95\%$ confident that not wearing helmets is related to accident casualties?

|         | Not Wearing Helmet | Wearing Helmet |
|---------|--------------------|----------------|
| Casualty | $7$                | $3$            |
| No Casualty | $13$             | $27$           |

Reference formula: $\hat{b}=\frac{\sum_{i=1}^{n}{x}_{i}{y}_{i}-n\overline{x}\overline{y}}{\sum_{i=1}^{n}{{x}_{i}}^{2}-n{\overline{x}}^{2}}=\frac{\sum_{i=1}^{n}({x}_{i}-\overline{x})({y}_{i}-\overline{y})}{\sum_{i=1}^{n}({x}_{i}-\overline{x})^{2}}$,$\hat{a}=\overline{y}-\hat{b}\overline{x}$.

| $P(K^{2}\geqslant k)$ | $0.10$ | $0.05$ | $0.025$ | $0.010$ | $0.005$ | $0.001$ |
|------------------------|--------|--------|---------|---------|---------|---------|
| $k$                    | $2.706$| $3.841$| $5.024$ | $6.635$ | $7.879$ | $10.828$|

$K^{2}=\frac{n{(ad-bc)}^{2}}{(a+b)(c+d)(a+c)(b+d)}$, where $n=a+b+c+d$.

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