Question

census data doe 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 this allarent under-representation of Hispanics call in to question the fairness of the jury selection system?

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 this apparent under-representation of Hispanics call in to question the fairness of the jury selection system? Explain. Recall that for this stated problem, our class decided to use an alpha-value (also called a significance-level) of a-11%. Our null hypothesis is Hop-19%, and our two-sided alternative hypothesis is HA:p#19%. The problem gives us X-9, n-72, p-hat-12.5%, and p-19% (per the null hypothesis). Since we are in the Binomial Setting, we have X-B(72, 0.19), and E(X-13.68 is the expected value of X. Note this means that our actual observation of X-9, fell 4.68 units away from the expected value E(X)-13.68 here Here it is: a) Using the approach shown in class and our given Binomial model: Find the probability of falling at least as far away from expected as we actually observed, meaning 4.68 or more away from 13.68 (in either direction). Note that the probability we find here, is called the P-value, and the process we are performing here is called a two-sided significance test. b) In any 2-sided significance test: If the P-value s alpha-value, we say that "we reject the null hypothesis in favor of the 2-sided alternative". But if instead, the P-value > alpha-value, we say that "we fail to reject the null hypothesis". Using your result from part (a) above: Choose which of these two statements we must conclude here, and write this statement (verbatim)

Answer 1

1. Null hypothesis: The null hypothesis is that the percentage of adult residents are Hispanic is 19%i.e.

   

   H() : p = 0.19

   Alternative hypothesis: The alternative hypothesis is that the percentage of the adult residents is Hispanic is less than 19% i.e.

   

   H p<0.19

   The conditions are given by,

   The sample is a simple random sample. And the sample is less than 10% of all the adult residents are Hispanic.

   The Success / Failure conditions are given by,
   nPo = 72(0.19)= 13.68210
   and
   no 72(0.81) 58.32 210
   .

2. Now, we can proceed further to do the test is given by,

   We have n = 72, X =9 and a hypothesized p = 0.19.

   

   

   97

   

   0.125

   And the

   1-P

   

   0.19(1-0.19) 72

   

   = 0.04623

   The z-score is given by,

   

   Po SD(P)

   

   0.125-0.19 0.04623

   

   -0.065 0.04623

   = -1.41

3. The P – Value is given by,

   

   P-value =P(z<-1.41)

   

   007 927

   Conclusion: Because of the P – Value is high, we do not reject the null hypothesis or we may fail to reject the null hypothesis with the sample data given. And hence we may conclude that there is not sufficient evidence that the proportion of the adult residents who are Hispanic is less than all the adult residents who are Hispanic. Yes, this is apparent underrepresentaion of Hispanics call into question the fairness of the jury selection system.

   Но