College

A teacher claims that on any given day, 60% of her students complete their homework and 40% do not. To investigate this belief, she randomly selects 30 of her 120 students and determines how many of them completed their homework that day and how many did not. She would like to know if her findings provide convincing evidence that the distribution of homework completion status differs from her original belief.

Are the conditions for inference met?

A. No, the random condition is not met.
B. No, the 10% condition is not met.
C. No, the Large Counts condition is not met.
D. Yes, all of the conditions for inference are met.

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:

  1. Random Condition: The teacher claims that she randomly selected 30 students. If this selection was indeed random, then this condition is met.
  2. 10% Condition: Since the sample of 30 students is less than 10% of the population of 120 students, this condition is satisfied as well.
  3. 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
    Since both counts exceed 10, this condition is also met.

After analyzing these conditions, we find that all conditions for inference are indeed met.


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