Respuesta :
Step-by-step explanation:
**I'm ready to address the chi-square test for the gender gap analysis. However, I need the table of responses from the poll to proceed with the calculations and conclusions.**
**Once you provide the table, I can guide you through the following steps:**
**i) Stating the hypotheses:**
* Null hypothesis (H0): There is no relationship between gender and voter opinion about the candidate (no gender gap).
* Alternative hypothesis (Ha): There is a relationship between gender and voter opinion about the candidate (gender gap exists).
**ii) Finding the critical value:**
* Determine the degrees of freedom (df) = (number of rows - 1) * (number of columns - 1).
* Choose a significance level (e.g., α = 0.05).
* Use a chi-square distribution table or calculator to find the critical value corresponding to α and df.
**iii) Constructing the table and calculating the test statistic:**
* Create a contingency table with rows for gender (male/female) and columns for voter opinion categories.
* Fill in the observed counts from the poll data.
* Calculate expected counts for each cell, assuming independence between gender and opinion.
* Calculate the chi-square test statistic using: χ2 = Σ [(observed count - expected count)^2 / expected count].
**iv) Stating a conclusion:**
* Compare the calculated χ2 value to the critical value.
* If χ2 > critical value, reject H0 and conclude there's a significant relationship (gender gap).
* If χ2 ≤ critical value, fail to reject H0 and conclude there's no significant evidence of a relationship.
**Please provide the table of responses so I can complete these steps and provide a comprehensive analysis.**