A Survey Conducted in a Small Business Yielded the Results

question 23

Essay

A survey conducted in a small business yielded the results shown in the table. $$\begin{array} { l | c c } & \text { Men}&\text { Women } \\\hline \text { Health insurance } & 50 & 20 \\\hline \text { No health insurance } & 30 & 10\end{array}$$ i) Test the claim that health care coverage is independent of gender. Use a 0.05
significance level.
ii) Using Yates' correction, replace $\sum { \frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { E } } \text { with } \sum { \frac { ( | \mathrm { O } - \mathrm { E } | - 0.5 ) ^ { 2 } } { E } }$ and repeat the test.
What effect does Yates' correction have on the value of the test statistic?

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Definitions:

Rapid Defense Response

An immediate response mechanism by organisms, particularly plants, to repel or mitigate damage from predators or pathogens.

Chronic Obstructive Pulmonary Disease

A group of lung conditions that cause breathing difficulties, including emphysema and chronic bronchitis, often due to long-term exposure to harmful substances.

Bronchial Constriction

The narrowing of the bronchi in the lungs due to the tightening of surrounding smooth muscle, often as a response to asthma or other respiratory conditions.

Pulmonary Emphysema

A chronic respiratory disease characterized by the destruction of the air sacs in the lungs, leading to difficulty in breathing.