A survey conducted in a small business yielded the results shown in the table. $\begin{array} { l c c } & \text { Men } & \text { Women } \ \text { Health insurance } & 50 & 20 \ \text { No health insurance } & 30 & 10 \end{array}$
Test the claim that health care coverage is independent of gender. Use a $0.05$ significance level. What is the value of the test statistic?
A) $\chi ^ { 2 } = 0.1637$
B) $\chi ^ { 2 } = 3.841$
C) $\chi ^ { 2 } = 8.263$
D) $\chi ^ { 2 } = 5.821$

Question

Quizplus · Accepted Answer

The test statistic $\chi^2 = 0.1637$ is calculated using the formula for the chi-square test of independence, which compares the observed frequencies to the expected frequencies under the assumption that health care coverage is independent of gender. The calculation involves summing the squared differences between observed and expected frequencies, divided by the expected frequencies, for each category. The low value of $\chi^2$ suggests a lack of significant association between health care coverage and gender, supporting the claim of independence at the $0.05$ significance level.

A Survey Conducted in a Small Business Yielded the Results