The fire department in a large city is examining its promotion policy to asses i

Question

The fire department in a large city is examining its promotion policy to asses if there is the potential for an age discrimination lawsuit. A random sample of 248 promotion decisions over the past 5 years yield the following information:

Based on the below information, is the age of the fireman related to whether or not the fireman is promoted? Use alpha = .05. The contingency table shows Count & Expected Count.

Age at Promotion Decision Promotion Decision 39 or younger 40 or Older Promoted 38 46 Not Promoted 80 84 Contingency Analysis of Promoted By Age at Promotion Decision Freq: Frequency Contingency Table Promoted Count Yes Under 3 40 or Older Yes No otal uinder:39 3880 118 c Expected al 39.9677 78.0323 · 46 84 130 44.032385.9677 otal 164248 Tests DF LogLike RSquare (U) 0.0009 248 1 0.13987972 Test Likelihood Ratio Pearson ChiSquare Prob> ChiSq 0.280 0.279 0.5969 0.5970 Fisher's Exact Test Left Right 2-Tail Prob Alternative Hypothesis 0.3470 Prob(Promoted: No) is greater for Age at Promotion Decision-Under 39 than 40 or Older 0.7461 Prob(Promoted No) is greater for Age at Promotion Decision 40 or Older than Under 39 0.6871 Prob(Promoted No) is different across Age at Promotion Decisiorn

Explanation / Answer

Ho: The promotion of fireman is not related to age.

H1: The promotion of fireman is related to age.

Here the value of chi-square statistic is 0.279 . The p-value is 0.5970 . Here p-value > Alpha , hence, we fail to reject the null hypothesis.

Conclusion : The promotion of fireman is not related to age.

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