Questions: (a) A flute instructor examined student progress. He found that playing a longer song does not necessarily mean that a student will have more or fewer wrong notes. What can he conclude? There is no correlation between song length and number of wrong notes. There is a correlation between song length and number of wrong notes. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between song length and number of wrong notes. There is probably also causation. This is because there is likely an increase in the number of wrong notes with an increase in the song length. (b) An environmental study was conducted. It reported that, for a park, having more visitors indicates having a larger number of trees. What can be determined? There is no correlation between number of visitors and number of trees. There is a correlation between number of visitors and number of trees. However, there is no causation. This is because there is an increase in the number of trees with an Increase in the number of visitors. There is a correlation between number of visitors and number of trees. There may or may not be causation. Further studies would have to be done to determine this. (c) Data was collected at a tennis court. It showed that being older implies that a player will stay for a shorter length of time. What is likely true? There is no correlation between age and length of stay. There is a correlation between age and length of stay. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between age and length of stay. However, there is no causation. This is because there is a decrease in the length of stay with an increase in age.

(a) A flute instructor examined student progress. He found that playing a longer song does not necessarily mean that a student will have more or fewer wrong notes. What can he conclude? There is no correlation between song length and number of wrong notes. There is a correlation between song length and number of wrong notes. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between song length and number of wrong notes. There is probably also causation. This is because there is likely an increase in the number of wrong notes with an increase in the song length. (b) An environmental study was conducted. It reported that, for a park, having more visitors indicates having a larger number of trees. What can be determined? There is no correlation between number of visitors and number of trees. There is a correlation between number of visitors and number of trees. However, there is no causation. This is because there is an increase in the number of trees with an Increase in the number of visitors. There is a correlation between number of visitors and number of trees. There may or may not be causation. Further studies would have to be done to determine this. (c) Data was collected at a tennis court. It showed that being older implies that a player will stay for a shorter length of time. What is likely true? There is no correlation between age and length of stay. There is a correlation between age and length of stay. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between age and length of stay. However, there is no causation. This is because there is a decrease in the length of stay with an increase in age.
Transcript text: (a) A flute instructor examined student progress. He found that playing a longer song does not necessarily mean that a student will have more or fewer wrong notes. What can he conclude? There is no correlation between song length and number of wrong notes. There is a correlation between song length and number of wrong notes. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between song length and number of wrong notes. There is probably also causation. This is because there is likely an increase in the number of wrong notes with an increase in the song length. (b) An environmental study was conducted. It reported that, for a park, having more visitors indicates having a larger number of trees. What can be determined? There is no correlation between number of visitors and number of trees. There is a correlation between number of visitors and number of trees. However, there is no causation. This is because there is an increase in the number of trees with an Increase in the number of visitors. There is a correlation between number of visitors and number of trees. There may or may not be causation. Further studies would have to be done to determine this. (c) Data was collected at a tennis court. It showed that being older implies that a player will stay for a shorter length of time. What is likely true? There is no correlation between age and length of stay. There is a correlation between age and length of stay. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between age and length of stay. However, there is no causation. This is because there is a decrease in the length of stay with an increase in age.
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Solution

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(a) The answer is: There is no correlation between song length and number of wrong notes.

Explanation:

  • There is no correlation between song length and number of wrong notes: This is the correct conclusion based on the information provided. The instructor found that playing a longer song does not necessarily mean more or fewer wrong notes, indicating no correlation.
  • There is a correlation between song length and number of wrong notes. There may or may not be causation: This option is incorrect because the instructor's findings suggest no correlation.
  • There is a correlation between song length and number of wrong notes. There is probably also causation: This is incorrect as the instructor's findings indicate no correlation, and thus, causation is not applicable.

(b) The answer is: There is a correlation between number of visitors and number of trees. There may or may not be causation. Further studies would have to be done to determine this.

Explanation:

  • There is no correlation between number of visitors and number of trees: This is incorrect because the study reported a relationship between the number of visitors and the number of trees.
  • There is a correlation between number of visitors and number of trees. However, there is no causation: This is not necessarily correct because the presence or absence of causation is not determined by the information given.
  • There is a correlation between number of visitors and number of trees. There may or may not be causation: This is the correct interpretation. The study shows a correlation, but further research is needed to establish causation.

(c) The answer is: There is a correlation between age and length of stay. There may or may not be causation. Further studies would have to be done to determine this.

Explanation:

  • There is no correlation between age and length of stay: This is incorrect because the data showed a relationship between age and length of stay.
  • There is a correlation between age and length of stay. There may or may not be causation: This is the correct interpretation. The data indicates a correlation, but further research is needed to determine if there is causation.
  • There is a correlation between age and length of stay. However, there is no causation: This is not necessarily correct because the presence or absence of causation is not determined by the information given.
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