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Evidence that Bank Supervisors Discriminated against Females

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Forty-eight male bank supervisors were each given the same personal file and asked to judge whether the person should be promoted to a branch manager job that was described as "routine", or the file held and other applicants interviewed.
The files were identical except that half of them showed that the file was that of a female and half showed that the file was that of a male. Of the 24 "male files", 21 were recommended for promotion. Of the 24 "female files", 14 were recommended for promotion.

Question- Is the information as published convincing evidence that the bank supervisors discriminated against female applicants, or could the difference in the number recommended for promotion reasonably attributed to chance? Explain.

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Solution Summary

The solution examines the evidence that the bank supervisors discriminated against female applicants. The difference in the number of recommended for promotion reasonably attributed to chance is determined.

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Forty-eight male bank supervisors were each given the same personal file and asked to judge whether the person should be promoted to a branch manager job that was described as "routine", or the file held and other applicants interviewed.
The files were identical except that half of them showed that the file was that of a female and half showed that the file was that of a male. Of the 24 "male files", 21 were recommended for promotion. Of the 24 "female files", 14 were recommended for promotion.

Question- Is the information as published convincing evidence that the bank supervisors discriminated against female ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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