To determine the outcome of the null hypothesis using the chi-square test, follow these detailed steps:
1. Chi-Square Value and Critical Value:
- Your chi-square value (obtained from the chi-square test) is 7.73.
- The critical value at a .05 level of confidence with one degree of freedom is 3.34.
2. Comparison:
- To interpret the result, compare the chi-square value with the critical value:
- If the chi-square value is greater than the critical value, we reject the null hypothesis.
- If the chi-square value is less than or equal to the critical value, we fail to reject the null hypothesis.
3. Analysis:
- Given that 7.73 (the chi-square value) is greater than 3.34 (the critical value), we have sufficient evidence to reject the null hypothesis.
4. Conclusion:
- Thus, the result of your null hypothesis test is: The null is rejected.
Therefore, according to your data and the critical value provided, the correct statement is:
- "The null is rejected."