In orange county 12 of those eligible for jury duty are left

In orange county 12% of those eligible for jury duty are left handed. Among 250 people selected for jury duty, 25 are lefties. Find the probability of getting at most 25 lefties assuming that they are chosen with a process designed to yield 12% rate of lefties. Can we conclude that this process of selecting jurors discriminates against lefties?

Solution

We assume the level of significnace to be 0.05, we it is not given.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.12
Ha:   p   <   0.12 [ANSWER]

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As we see, the hypothesized po =   0.12      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.1      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.020552372      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -0.97312368      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.165245918      

significance level =    0.05      

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

Thus, there is no significant evidence that this process of selecting jurors discriminates against lefties. [CONCLUSION]