a convicted man appealed his conviction based on the claim that he was not tried

Question

a convicted man appealed his conviction based on the claim that he was not tried by a jury of his peers. census data for a certain county show that 19% of the adult residents are hispanic. suppose 72 people are called for jury duty and only 9 of them are hispanic. does that apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? perform this test using the p-value approach at teh 5% significance level. A. state the null and alternative hypothesis, find the p-VAlue, does the convicted person win his appeal or have to go back to jail ?

Explanation / Answer

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.19
Ha:   p   <   0.19 [HYPOTHESES]

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As we see, the hypothesized po =   0.19      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.125      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.046233105      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.405918983      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.079874092   [P VALUE]

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As P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Hence, the convicted person have to go to jail. He has no significant evidence that Hispanics are underrepresented in this case. [CONCLUSION]  

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