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There is a correlation between the scores on a national math assessment and the number of hours students spent on preparing for the assessment.

​​​​​Which of the following statements are true? Check all that apply.

Based upon the study, a student who gets more sleep before the assessment should expect a higher score.

A value of r=-.88 is a reasonable measurement for the correlation coefficient of this association.

There is causation between the amount of time students spent preparing and their scores on the national math assessment.

The correlation between the two quantities should be fairly strong to strong.

A value of 2.35 could be a reasonable slope for the function equation.

1 answer

Let's analyze each statement individually based on the information provided about the correlation between scores on a national math assessment and the number of hours students spent preparing for the assessment.

  1. "Based upon the study, a student who gets more sleep before the assessment should expect a higher score."

    • False: While sleep can impact cognitive performance, this statement makes an assumption about a causal relationship that isn't inherently supported by the correlation between preparation hours and assessment scores. The study focuses on preparation time, not sleep.

  2. "A value of r=-.88 is a reasonable measurement for the correlation coefficient of this association."

    • False: A correlation coefficient of -0.88 suggests a strong negative correlation, which would imply that as preparation hours increase, scores decrease. Given the context (more preparation usually leads to better scores), a positive correlation is expected. Therefore, a value of r=-.88 would not be reasonable.

  3. "There is causation between the amount of time students spent preparing and their scores on the national math assessment."

    • False: Correlation does not imply causation. While there may be an association between hours spent preparing and scores, it does not mean that more preparation directly causes higher scores; other factors might be involved.

  4. "The correlation between the two quantities should be fairly strong to strong."

    • True: Given that the statement mentions a correlation exists between preparation hours and scores, it is likely that the correlation observed would be reasonably strong, especially if students tend to improve their scores with more preparation.

  5. "A value of 2.35 could be a reasonable slope for the function equation."

    • True/False: Without additional context on the data points or regression analysis performed, this statement cannot be definitively assessed as true or false. However, a positive slope could make sense if we assume that more hours of preparation lead to higher scores. A slope of 2.35 may or may not be reasonable, depending on the actual data.

Summary:

  • True: The correlation should be fairly strong to strong.
  • False: The other statements about causation, the value of r, and the assumptions about sleep. The last statement would need further context for a definitive answer.