To analyze the relative frequency table provided, we can summarize the information:
- 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, we will evaluate each of the responses given:
-
More fourth graders responded than third graders.
- This statement can't be fully determined just from the relative frequencies. We don’t know the total number of third graders or fourth graders to make this comparison. This statement cannot be confirmed.
-
Most students in the sample have a pet.
- To see if most students have a pet, look at the total percentage who have a pet: 45%. Since this is less than 50%, this statement is incorrect.
-
The smallest joint relative frequency is third graders without a pet.
- The joint relative frequency for third graders without a pet is 19%. The smallest joint relative frequency is actually for third graders with a pet (16%). Therefore, this statement is incorrect.
-
The largest joint relative frequency is fourth graders with a pet.
- The joint relative frequency for fourth graders with a pet is 29%. This is not the largest; the largest is for fourth graders without a pet (36%). Thus, this statement is incorrect.
Based on this analysis, none of the responses are accurate. There are issues in all options, but the closest correct observation related to the data is that "More fourth graders without pets than third graders without pets," though that statement is not one of the provided options.
In summary, each of the provided interpretations is incorrect based on the data given.