Descriptive Statements:
- Use appropriate formats for collecting, organizing, and displaying quantitative and qualitative data.
- Analyze data in a variety of representations (e.g., histograms, two-way tables, scatterplots, box and whisker plots).
- Analyze and compare measures of central tendency and variability (e.g., mean absolute deviation, interquartile range, standard deviation).
- Analyze the effects of bias and sampling techniques.
- Analyze probability distributions (e.g., skewed, uniform, normal).
- Interpret the correlation coefficient and distinguish between correlation and causation.
Sample Item:
Researchers conducted a study comparing the populations of foxes and rabbits in a state park. The researchers determined that the relationship between the population of rabbits, x, and foxes, y, can be modeled by the regression equation y = –1.05x + 1,754.04 y equals negative 1.05 x plus 1754.04 , with a correlation coefficient of – negative 0.91. Which of the following statements correctly interprets the correlation coefficient?
- There is a strong correlation between the populations of the two animals, and the population of rabbits decreases as the population of foxes increases.
- There is a strong correlation between the populations of the two animals, and the population of rabbits increases as the population of foxes increases.
- There is a weak correlation between the populations of the two animals, and the population of rabbits decreases as the population of foxes increases.
- There is a weak correlation between the populations of the two animals, and the population of rabbits increases as the population of foxes increases.
Correct Response and Explanation (Show Correct ResponseHide Correct Response)
A. A negative correlation coefficient implies that as the independent variable (rabbit population) increases, the dependent variable (fox population) decreases. Additionally, a correlation coefficient with an absolute value close to 1 indicates a strong correlation between the variables. A correlation coefficient of – negative 0.91, therefore, represents a strong correlation between the populations and one where a decrease in the rabbit population is associated with an increase in the population of foxes.
Descriptive Statements:
- Determine probabilities of simple and compound events and conditional probabilities.
- Calculate probabilities and solve problems using counting principles (e.g., the fundamental counting principle, factorials, permutations, combinations) and set theory.
- Use a variety of models to identify the size of the sample space for an event and calculate probabilities for an event (e.g., tree diagram, frequency table).
- Select simulations that model real-world events and predict possible outcomes.
- Calculate and interpret expected value from a discrete probability distribution.
Sample Item:
If two fair number cubes are rolled, what is the probability that the sum of the outcome is less than 5?
1 ninth 
1 sixth 
1 fourth 
5 eighteenths
Correct Response and Explanation (Show Correct ResponseHide Correct Response)
B. There are 6 • 6 = 36 6 times 6 equals 36 outcomes in the sample space for two fair number cubes. Of these, the rolls (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), and (3, 1) have a sum of less than 5. The probability of one of these outcomes occurring is therefore 
6 over 36 equals 1 over 6 .
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