What factors should the assistant chief consider in determining the presence of gender bias in firefighter promotion? Is the promotional status of recently promoted firefighters independent of their gender?

You volunteer some of your spare time to your local fire department and have been asked by an assistant chief to analyze data on firefighters who applied for promotion. The assistant chief wants to ensure that gender bias is not a concern in the promotion of firefighters. Shown below is data for 50 firefighters who applied for promotion and the results of a chi-square analysis of the data.

Male
Female
Promoted
13
22
Not Promoted
10
5

Chi-Square Statistic
3.6845
P value
0.054919

What factors should the assistant chief consider in determining the presence of gender bias in firefighter promotion?
Is the promotional status of recently promoted firefighters independent of their gender?
What reasons should the assistant chief convey to the fire chief to justify the absence of gender bias in the most recent class of firefighters who were promoted?
How might the presence of gender bias in promotions impact the fire department?

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