In Exercises 13–20, determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance.

Bias in Jury Selection In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty, and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry.

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Identify the null hypothesis (H0) and the alternative hypothesis (H1). In this case, H0: The proportion of Americans of Mexican ancestry selected for jury duty is equal to the proportion eligible (p = 0.791). H1: The proportion of Americans of Mexican ancestry selected for jury duty is not equal to the proportion eligible (p ≠ 0.791).

Calculate the sample proportion (p̂) of Americans of Mexican ancestry selected for jury duty. This is given as 39%, or 0.39.

Determine the sample size (n), which is the total number of people selected for jury duty. In this case, n = 870.

Use the formula for the standard error of the sample proportion: SE = sqrt((p * (1 - p)) / n), where p is the population proportion (0.791) and n is the sample size (870).

Calculate the z-score using the formula: z = (p̂ - p) / SE, where p̂ is the sample proportion (0.39), p is the population proportion (0.791), and SE is the standard error calculated in the previous step. Compare the z-score to a critical value from the standard normal distribution to determine statistical significance. Consider practical significance by evaluating the real-world impact of the difference in proportions.

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주요 개념

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Statistical Significance

Statistical significance refers to the likelihood that a result or relationship is caused by something other than mere random chance. In the context of jury selection, it involves determining if the observed proportion of Americans of Mexican ancestry selected for jury duty significantly deviates from the expected proportion based on the eligible population. This is typically assessed using hypothesis testing and p-values.

Practical Significance

Practical significance considers whether a statistically significant result has real-world implications or importance. Even if a result is statistically significant, it may not be practically significant if the effect size is too small to matter in a real-world context. In the jury selection case, practical significance would assess whether the difference in proportions has meaningful consequences for the fairness of the jury selection process.

Bias in Jury Selection

Bias in jury selection refers to systematic favoritism or discrimination in the process of selecting jurors, which can lead to unrepresentative juries. In Casteneda v. Partida, the potential bias is evaluated by comparing the proportion of Americans of Mexican ancestry selected for jury duty to the proportion eligible, highlighting discrepancies that may indicate discriminatory practices. Understanding bias is crucial for ensuring equitable legal proceedings.