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Answer :
To determine if the conditions for inference are met for the given data related to berry snack packs, we need to check three specific statistical conditions:
1. Random Sample Condition:
- The data should be collected from a random sample. However, based on the problem description provided, we do not have enough information to verify this condition. Without this information, we cannot affirmatively state that the data come from a random sample.
2. 10% Condition:
- This condition checks if the sample sizes are less than 10% of the total population, ensuring that the sample is small enough not to affect the overall distribution.
- For Brand A, the total number of samples is 23 (8 Strawberry + 10 Raspberry + 5 Blueberry). Checking against a hypothetical population size, our answer indicates a value of 2.3 when calculating 10% of a presumed population. Since 23 is not less than 2.3, the 10% condition is not met for Brand A.
- For Brand B, the total number of samples is 21 (4 Strawberry + 14 Raspberry + 3 Blueberry). Similarly, the answer indicates a value of 2.1 for 10% of a population, but 21 is not less than 2.1, so the 10% condition is not met for Brand B as well.
3. Large Counts Condition:
- We calculate the expected counts for each berry type in each brand to ensure they are all greater than 5. The expected count is derived from the product of the marginal totals divided by the grand total.
- The expected counts for Brand A are 6.27 for Strawberry, 12.55 for Raspberry, and 4.18 for Blueberry. For Brand B, these values are 5.73 for Strawberry, 11.45 for Raspberry, and 3.82 for Blueberry.
- The Large Counts condition requires all expected counts to be greater than 5. However, the calculations reveal not all expected counts are greater than 5. Specifically, the expected counts for Blueberry in both brands are less than 5.
In summary, given the detailed assessment:
- The Random Sample Condition cannot be confirmed.
- The 10% Condition is not satisfied for both brands.
- The Large Counts Condition is not satisfied because not all expected counts are greater than 5.
Therefore, we conclude that the conditions for inference are not fully met for the given data.
1. Random Sample Condition:
- The data should be collected from a random sample. However, based on the problem description provided, we do not have enough information to verify this condition. Without this information, we cannot affirmatively state that the data come from a random sample.
2. 10% Condition:
- This condition checks if the sample sizes are less than 10% of the total population, ensuring that the sample is small enough not to affect the overall distribution.
- For Brand A, the total number of samples is 23 (8 Strawberry + 10 Raspberry + 5 Blueberry). Checking against a hypothetical population size, our answer indicates a value of 2.3 when calculating 10% of a presumed population. Since 23 is not less than 2.3, the 10% condition is not met for Brand A.
- For Brand B, the total number of samples is 21 (4 Strawberry + 14 Raspberry + 3 Blueberry). Similarly, the answer indicates a value of 2.1 for 10% of a population, but 21 is not less than 2.1, so the 10% condition is not met for Brand B as well.
3. Large Counts Condition:
- We calculate the expected counts for each berry type in each brand to ensure they are all greater than 5. The expected count is derived from the product of the marginal totals divided by the grand total.
- The expected counts for Brand A are 6.27 for Strawberry, 12.55 for Raspberry, and 4.18 for Blueberry. For Brand B, these values are 5.73 for Strawberry, 11.45 for Raspberry, and 3.82 for Blueberry.
- The Large Counts condition requires all expected counts to be greater than 5. However, the calculations reveal not all expected counts are greater than 5. Specifically, the expected counts for Blueberry in both brands are less than 5.
In summary, given the detailed assessment:
- The Random Sample Condition cannot be confirmed.
- The 10% Condition is not satisfied for both brands.
- The Large Counts Condition is not satisfied because not all expected counts are greater than 5.
Therefore, we conclude that the conditions for inference are not fully met for the given data.
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