When a study was conducted on the demographic makeup of Huge

When a study was conducted on the demographic make-up of HugeCorp, it had been determined that 50% of it\'s employees were women; however, it was also determined that out of 80 employees in upper management, 47 were women. Assuming that HugeCorp only promotes current employees, at the 82% level of confidence, does it seem as though HugeCorp\'s promotion practices are discriminatory (against men or women)?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   =/=   0.5
As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.5875      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.055901699      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.565247584      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.117524868      
significance level =    0.18      

Comparing p and the significance value, we   REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence at 82% confidence that HugeCorp\'s promotion practices are discriminatory. [CONCLUSION]

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Note: an 82% confidence is very unusual. If this is a typo error, please resubmit this question together with the correction. That way we can continue helping you! Thanks!