Chi-Squared Exercise Name: _________________________________ ✓ Solved

Chi-Squared Exercise Name: _______________________________________

Subjects are inmates incarcerated in Louisiana’s only prison for female offenders. A total of 119 subjects participated in the study. The research question is: “In adult women incarcerated in Louisiana, is there a difference in types of crime committed across marital status groups?” Data collected is noted in Table 1.

1. State the null hypothesis for the research question above.

2. State the rationale for running a chi-squared test on this data.

3. Create Table 1 in Excel. Run a chi-squared test. Show all of your work.

4. Using a P-value of 0.05, should the null hypothesis be rejected? Explain.

5. Report your chi-squared conclusion including the degrees of freedom and X2 = 24.27.

Paper For Above Instructions

The focus of this study revolves around female inmates in Louisiana and aims to explore the relationship between marital status and the types of crimes committed. The chi-squared statistical method offers a means to assess whether a significant relationship exists between categorical variables, particularly when analyzing the characteristics of a population based on specific demographic variables. In this case, we can structure our response as follows:

1. Null Hypothesis

The null hypothesis (H0) for the stated research question is: "There is no significant difference in the types of crimes committed across different marital status groups among adult women incarcerated in Louisiana." This hypothesis suggests that the distribution of crime types is independent of marital status. In statistical terms, any observed differences would be due to chance rather than a true association.

2. Rationale for Using Chi-Squared Test

The rationale for employing a chi-squared test in this study lies in the nature of the data collected, which is categorical (marital status and type of crime). Chi-squared tests are appropriate for examining relationships between two categorical variables. This test allows us to evaluate the frequency distribution of the observed data against expected frequencies under the null hypothesis, thereby facilitating a determination of whether the differences observed are statistically significant.

3. Creation of Table 1 and Chi-Squared Test Analysis

Table 1 can be constructed in Excel with appropriate columns for types of crimes (e.g., murder, robbery, theft, drugs) versus marital status categories (single, previously married, married). The chi-squared test should then be performed using the data collected. This involves calculating the expected frequencies, applying the chi-squared formula, and determining if the computed chi-squared statistic exceeds the critical value for the chosen significance level (p

For instance, if the observed and expected frequencies are known, the chi-squared statistic can be calculated as:

Χ² = Σ((Observed - Expected)² / Expected)

With degrees of freedom (df) calculated as:

df = (number of rows - 1) * (number of columns - 1)

4. Decision on the Null Hypothesis

With a p-value of 0.05, the null hypothesis should be rejected if the calculated p-value is less than 0.05. If the chi-squared statistic calculated is significant, it indicates that the differences among the types of crimes across the marital status groups are statistically significant and not due to random chance.

5. Reporting Chi-Squared Conclusion

Upon conducting the chi-squared test, suppose the calculated statistic X² equals 24.27. The degrees of freedom (df) would depend on the number of categories in both variables (e.g., degrees of freedom = (3-1)(3-1) = 4 for three types of crimes and three marital status categories). If the critical value for chi-squared with the appropriate degrees of freedom is less than 24.27 at p

Conclusion

This analysis underscores the importance and utility of the chi-squared test in assessing differences in categorical data, especially in sensitive areas such as crime and marital status in female populations. The implications of these findings can inform policy changes and support systems for female offenders, aiming to address underlying factors related to their criminal behavior.

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