Recent court case found that during a period of 11 years 891 people were selecte
ID: 3159874 • Letter: R
Question
Recent court case found that during a period of 11 years 891 people were selected for grand jury duty & 42% were the same ethnicity. Among the people eligible 80% were of this ethnicity. Use 0.05 significance level to test claim that the selection process is biased against allowing ethnicity to sit on the grand jury. Identify the null hypothesis, alternate hypothesis, test statistic, P- value, conclusion about the null hypothesis & the final conclusion that addresses the original claim. Use the P- value method & the normal distribution as an approximation to the binomial distribution.
Explanation / Answer
Formulating the null and alternatuve hypotheses,
Ho: p >= 0.8
Ha: p < 0.8 [HYPOTHESES]
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As we see, the hypothesized po = 0.8
Getting the point estimate of p, p^,
p^ = x / n = 0.42
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.013400504
Getting the z statistic,
z = (p^ - po)/sp = -28.35714196 [TEST STATISTIC]
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As this is a 1 tailed test, then, getting the p value,
p = 3.417*10^-177 [P VALUE]
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As P < 0.05, we REJECT THE NULL HYPOTHESIS.
There is significant evidence that the selection process is biased against allowing ethnicity to sit on the grand jury. [CONCLUSION]
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