Answer :
To determine if the conditions for inference are met, we need to verify three specific conditions: the Random Condition, the 10% Condition, and the Large Counts Condition. Let's go through each one step-by-step:
1. Random Condition:
- This condition checks if the sample is randomly selected.
- In the provided problem, it states that a random sample was selected for both peak hours and off-peak hours. Therefore, the Random Condition is met.
2. 10% Condition:
- This condition ensures that the sample size is less than 10% of the population. This is important to ensure independence of the data.
- For peak hours, 100 customers were sampled. Therefore, the population of all possible peak hour customers should be more than 1,000 customers for this condition to hold.
- For off-peak hours, 70 customers were sampled, so the population of all possible off-peak customers should be more than 700 customers for this condition to hold.
- Since the condition is verified and these sample sizes are realistically less than or equal to 10% of the total populations, we can say the 10% Condition is met.
3. Large Counts Condition:
- This condition requires that the expected counts for each category in a categorical distribution are at least 5. This ensures appropriate sample size for the chi-square or other inference tests.
- Checking counts for Peak: All of the ratings (5, 8, 12, 40, 35) are greater than or equal to 5.
- Checking counts for Off-Peak: All of the ratings (13, 5, 16, 21, 15) are greater than or equal to 5.
- Therefore, all counts are above 5, satisfying the Large Counts Condition.
Based on these assessments, all three conditions for inferential statistics are satisfied. Thus, we can conclude that:
Yes, all three conditions for inference (Random Condition, 10% Condition, and Large Counts Condition) are met.
1. Random Condition:
- This condition checks if the sample is randomly selected.
- In the provided problem, it states that a random sample was selected for both peak hours and off-peak hours. Therefore, the Random Condition is met.
2. 10% Condition:
- This condition ensures that the sample size is less than 10% of the population. This is important to ensure independence of the data.
- For peak hours, 100 customers were sampled. Therefore, the population of all possible peak hour customers should be more than 1,000 customers for this condition to hold.
- For off-peak hours, 70 customers were sampled, so the population of all possible off-peak customers should be more than 700 customers for this condition to hold.
- Since the condition is verified and these sample sizes are realistically less than or equal to 10% of the total populations, we can say the 10% Condition is met.
3. Large Counts Condition:
- This condition requires that the expected counts for each category in a categorical distribution are at least 5. This ensures appropriate sample size for the chi-square or other inference tests.
- Checking counts for Peak: All of the ratings (5, 8, 12, 40, 35) are greater than or equal to 5.
- Checking counts for Off-Peak: All of the ratings (13, 5, 16, 21, 15) are greater than or equal to 5.
- Therefore, all counts are above 5, satisfying the Large Counts Condition.
Based on these assessments, all three conditions for inferential statistics are satisfied. Thus, we can conclude that:
Yes, all three conditions for inference (Random Condition, 10% Condition, and Large Counts Condition) are met.
