Answer :
Final answer:
All conditions for making statistical inferences about the distribution of homework completion are met in this case. The random selection of students satisfies the random condition, the sample size does not exceed 10% of the population, and the expected successes and failures meet the large counts condition. Thus, the teacher can conclude about the homework completion rates confidently.
Explanation:
Analysis of Conditions for Inference
To determine if the teacher's findings regarding homework completion can be considered convincing evidence that the distribution differs from her belief of 60% completion, we need to check if all conditions for inference are satisfied. The relevant conditions here include:
- Random Condition: The teacher claims that she randomly selected 30 students. If this selection was indeed random, then this condition is met.
- 10% Condition: Since the sample of 30 students is less than 10% of the population of 120 students, this condition is satisfied as well.
- Large Counts Condition: For inference procedures concerning proportions, the success and failure counts should both be at least 10. If we expect 60% of the 120 students to complete their homework, then:
- Expected successes: 0.6 120 = 72
- Expected failures: 0.4 120 = 48
After analyzing these conditions, we find that all conditions for inference are indeed met.
Learn more about Conditions for Inference here:
https://brainly.com/question/30090160