To analyze the options provided based on the given relative frequency table, let's look at the values:
- Third Graders with a Pet: 16%
- Third Graders without a Pet: 19%
- Fourth Graders with a Pet: 29%
- Fourth Graders without a Pet: 36%
Now, let's evaluate each statement:
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The largest joint relative frequency is fourth graders with a pet.
- This is incorrect. The largest relative frequency overall for fourth graders is 36% (those without a pet).
-
More fourth graders responded than third graders.
- This statement is not directly supported by the information given in the table, as we do not have absolute counts.
-
Most students in the sample have a pet.
- This is incorrect. Total percentage of students who have a pet (45%) is less than those who do not (55%).
-
The smallest joint relative frequency is third graders without a pet.
- This is correct. The smallest joint relative frequency is 16% for third graders with a pet, but 19% for third graders without a pet, which is larger than 16%. Therefore, there is no correct assertion regarding "smallest relative frequency" as applied to the paired groups.
After analyzing the statements, none of the interpretations accurately reflects the data from the provided table given their specific assessments.
Conclusion: The correct interpretation is actually not one of the provided statements based on the information available.
However, if forced to choose, "The largest joint relative frequency" should have been worded differently, as 36% is the highest value. The option referring to this statement as "the largest frequency" could be seen as somewhat correct if worded accurately, but still incorrect as stated due to the confusion about what was being asked.
Overall, the best answer based on logical evaluation is that while there might be an interpretation that sounds valid, none are actually accurately fitting based on the provided statistics.