Question

In a recent court case it was found that during la period of ll years 850 people were selected for grond jury duty and 38% of them were from the Same ethnicity. Among the people eligible for grond Jung duty, 78.2% were of this ethnicity. Use ao Significance level to test the claim that the selection process is biased agaisnt allowing ethnicity to sit on the grand jury. Av Identify null hypotheses and alternative. B.) Test statistic C) P-value D.) Conclusion about pull hypotheses E.) final conclusion that addresses original claim. this

Answer 1

In this court case, we can use a hypothesis test to determine if there is evidence to support the claim that the selection process for grand jury duty is biased against a certain ethnicity. Here are the steps to perform the hypothesis test:

a) Identify the null and alternative hypotheses:

The null hypothesis (H0​) is that the proportion of people from a certain ethnicity selected for grand jury duty is equal to the proportion of people from that ethnicity who are eligible for grand jury duty. In other words, H0​:p=0.782.

The alternative hypothesis (Ha​) is that the proportion of people from a certain ethnicity selected for grand jury duty is not equal to the proportion of people from that ethnicity who are eligible for grand jury duty. In other words, Ha​:p=0.782.

b) Calculate the test statistic:

The test statistic for a hypothesis test about a population proportion is given by the formula z=np0​(1−p0​)​​p^​−p0​​, where p^​ is the sample proportion, p0​ is the hypothesized population proportion under the null hypothesis, and n is the sample size.

In this case, p^​=0.38, p0​=0.782, and n=850. Plugging these values into the formula above, we get z≈−23.57.

c) Calculate the p-value:

The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated, assuming that the null hypothesis is true.

Since this is a two-tailed test (because the alternative hypothesis is p=0.782), we need to calculate the probability of observing a test statistic less than or equal to -23.57 or greater than or equal to 23.57.

Using a standard normal table or calculator, we find that this probability is very close to 0.

d) Conclusion about the null hypothesis:

Since the p-value is very small (less than any reasonable significance level), we reject the null hypothesis.

This means that there is strong evidence to suggest that the proportion of people from a certain ethnicity selected for grand jury duty is not equal to the proportion of people from that ethnicity who are eligible for grand jury duty.

e) Final conclusion:

Based on this hypothesis test, we can conclude that there is strong evidence to support the claim that the selection process for grand jury duty is biased against allowing people from this certain ethnicity to sit on the grand jury.