census data doe a certain county show that 19% of the adult residents are hispanic. suppose 72 people are called for ju…
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Question “census data doe a certain county show that 19% of the adult residents are hispanic. suppose 72 people are called for ju…”
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
Null hypothesis The null hypothesis states that 19% of adult residents in the United States are Hispanic.
Alternate hypothesis: Another hypothesis is that less than 19% of adult residents are Hispanic, i.e.
These conditions apply to,
This is a random sample. The sample includes less than 10% of the adult residents who are Hispanic.
We can now proceed to the next step, which is to take the test given by.
We have n =72, X =9, and a hypothesized 0.19.
The z-score is calculated by
= -1.41
The P-value is calculated by
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. We may conclude that the Hispanic adult residents are less than the total Hispanic adult residents. This is an apparent underrepresentation of Hispanics, which calls into question the fairness and fairness of jury selection.
Conclusion
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