Answer :
To determine whether the conditions for inference are met in the context of a Chi-Square Test of Association/Independence, we need to check a few conditions:
1. Random Sample: The data should come from a simple random sample. Since we do not have detailed information about the sampling method, we'll assume the data were collected randomly.
2. 10% Condition: The sample size should not exceed 10% of the population. This condition ensures that the sample is small enough not to affect the population calculations significantly. We assume this condition is satisfied if not otherwise specified.
3. Large Counts Condition: All expected frequencies should be greater than or equal to 5. This condition is important because the chi-square approximation to the distribution of the test statistic is only valid when the expected counts are sufficiently large.
In this problem, the calculation of expected frequencies and checking the Large Counts Condition is crucial. Let’s look at the table with observed frequencies:
- Brand A: Strawberry (8), Raspberry (10), Blueberry (5)
- Brand B: Strawberry (4), Raspberry (14), Blueberry (3)
After calculating the expected frequencies, we found that not all of them are greater than 5. Therefore, the Large Counts Condition is not met, which means the chi-square test's approximation might not be reliable.
Given this analysis, here are the conclusions:
- The Random Sample condition is assumed to be met because there's no contrary information.
- The 10% Condition is assumed to be met similarly.
- The Large Counts Condition is not met as not all expected frequencies are greater than 5.
Since the Large Counts Condition is not satisfied, not all conditions necessary for proper inference are met. Therefore, the answer to whether the conditions for inference are met is No, the Large Counts condition is not met since some expected counts are not greater than 5.
1. Random Sample: The data should come from a simple random sample. Since we do not have detailed information about the sampling method, we'll assume the data were collected randomly.
2. 10% Condition: The sample size should not exceed 10% of the population. This condition ensures that the sample is small enough not to affect the population calculations significantly. We assume this condition is satisfied if not otherwise specified.
3. Large Counts Condition: All expected frequencies should be greater than or equal to 5. This condition is important because the chi-square approximation to the distribution of the test statistic is only valid when the expected counts are sufficiently large.
In this problem, the calculation of expected frequencies and checking the Large Counts Condition is crucial. Let’s look at the table with observed frequencies:
- Brand A: Strawberry (8), Raspberry (10), Blueberry (5)
- Brand B: Strawberry (4), Raspberry (14), Blueberry (3)
After calculating the expected frequencies, we found that not all of them are greater than 5. Therefore, the Large Counts Condition is not met, which means the chi-square test's approximation might not be reliable.
Given this analysis, here are the conclusions:
- The Random Sample condition is assumed to be met because there's no contrary information.
- The 10% Condition is assumed to be met similarly.
- The Large Counts Condition is not met as not all expected frequencies are greater than 5.
Since the Large Counts Condition is not satisfied, not all conditions necessary for proper inference are met. Therefore, the answer to whether the conditions for inference are met is No, the Large Counts condition is not met since some expected counts are not greater than 5.
