Because of this, the variability in the sampling distribution of b , the estimator for the slope of the regression line, will be smaller for the first study plan with four observations at 6 feet and four observations at 13 feet than it would be for the second study plan with four observations at 8 feet and four observations at 10 feet. Therefore, the first study plan on the top would provide a better estimator of the slope of the regression line than the second study plan on the bottom.
Although this assumption was motivated by prior experience, it may not be correct. Describe another way of choosing the widths of the buffer strips at eight locations that would enable the researchers to check the assumption of a straight-line relationship. To assess the linear relationship between width of the buffer strip and the amount of nitrogen removed from runoff water, more widths should be used. To detect a nonlinear relationship, it would be best to use buffer widths that were spaced out over the entire range of interest.
For example, if the range of interest is 6 to 13 feet, eight buffers with widths 6, 7, 8, 9, 10, 11, 12 and 13 feet could be used. As you look back on this question in its entirety, consider the number of mental transitions that a student would need to make in order to navigate all six parts of the question successfully. Well-prepared AP Statistics students should be able to interpret the slope of a linear regression model in context in part a , and to explain why extrapolation is inappropriate in part b.
Students need to shift their thinking to the underlying assumption that the values of the response variable are normally distributed about the regression line at each value of the explanatory variable prior to parts c and d.
The novel reasoning required in part e is typical of the investigative task. To answer this part correctly, students need to recognize how the slopes could vary with each of the proposed study plans. Part f requires students to pivot one final time in considering a different aspect of the design: how to establish whether the relationship between the variables is linear. I suspect that many statistics teachers would have difficulty making all the moves expected in the last four parts of this question!
In the directions that precede the investigative task, students are reminded that the quality of their response includes both statistical accuracy and clear communication. Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. Rather than providing separate sub-scores for each of the six parts of this question, readers are instructed to group parts a and b into a single component, and parts c and d into a single component, with parts e and f counting as one component each.
Scoring This question is scored in four sections. Section 1 consists of parts a and b ; section 2 consists of parts c and d ; section 3 consists of part e ; section 4 consists of part f.
Each of the four sections is scored as essentially correct E , partially correct P , or incorrect I. The E-P-I scoring system for individual components of questions was another clever invention in the early years of the AP Statistics exam. Partially correct P is a broad category that acknowledges a wide range of student answers that include some, but not all, of the required statistical elements, or that suffer from weak communication. Recall that Section 1 consists of part a —interpreting the slope of the regression line in context—and part b —explaining why it is not appropriate to use the model to make predictions far outside the domain of values for the explanatory variable in this study.
Section 1 is scored as follows: Essentially correct E if the response includes the following two components: 1. The response in part a is correct, as evidenced by the correct interpretation of the slope, in context. The response in part b is correct, as evidenced by the identification of extrapolation as the reason that the model should not be used and the response is in context. It is quite common for question teams to provide additional scoring notes like the ones above to assist readers in applying the rubric consistently for each component of a question.
The first note was a direct result of seeing many student papers that gave a deterministic interpretation of slope like one might expect in a high school algebra course: the change in y that would occur for a one unit increase in x.
You can picture exam readers who might have different instincts about what to do in case of a student response that omitted units. The second note takes care of that issue.
Recall that Section 2 consists of parts c and d. Section 2 is scored as follows: Essentially correct E if the response includes the following two components: 1. The response in part c states that the sampling distribution is normal and provides a correct mean and standard deviation. The response in part d uses the correct mean and standard deviation of the sampling distribution—or incorrect values carried over from part c —and a correct critical value 1. Once again we see notes to help the exam readers make consistent decisions about how to score this section.
Now we move to the more investigative aspects of the question: parts e and f. Recall that part e asked students to choose which of two study plans would give a more precise estimate of the slope of the regression line for predicting amount of nitrogen removed from the runoff water y from the width of grass buffer strips x.
The figure below reminds you what students needed to think about in order to compose an essentially correct response. Section 3 of the scoring guidelines addresses part e. Section 3 is scored as follows: Essentially correct E if study plan 1 is chosen in part e , and the response demonstrates awareness of sampling variation in the estimates of the slopes of the regression lines, and this is clearly communicated in the context of the two study plans.
Partially correct P if study plan 1 is chosen in part e , and the response demonstrates awareness of sampling variation in the estimates of the slopes of the regression lines, but the justification of the choice of study plan 1 is not clearly communicated. In part f , students were expected to propose an alternative design for the study that would make it easier to determine if the relationship between x and y is linear.
Section 4 of the scoring guidelines covers this part of the question. Section 4 is scored as follows: Essentially correct E if the response specifies another study plan that uses eight buffer strips of at least three different specified widths, and the response indicates in how many locations each width will be used, or the response makes it clear that at least three different buffer widths will be used, and indicates that the buffer widths to be used will be spread out over the range of interest.
Partially correct P if the response does not meet criteria for E, but the stated plan uses at least three different widths. Widths need not be specified for a P. How does this set of four letter-scores get converted into an overall score for the question? The scoring guidelines include the following conversion guide. Each essentially correct E section counts as one point. Each partially correct P section counts as one-half point. If a response is between two scores for example, two and one-half points , use a holistic approach to decide whether to score up or down, depending on the overall strength of the response and communication.
The most challenging questions for students required Skill Category 3, Using Probability and Simulation. Scores would have been significantly higher if students performed this skill as well as they performed Skill Categories 1 and 2. Free-response section:. Close Site Navigation. AP Statistics Exam: Results. Trevor Packer July 27, Free-response section: The strongest results were typically on Question 4 and Question 6.
They explain that you should be familiar with the following topics:. For a comprehensive content review, check out our line of AP guides. Students are given exactly one hour and 30 minutes to complete the 40 questions in this part of the exam.
Each question will be followed by five answer choices. At times, it may seem that there could be more than one possible correct answer. There is only one! Answers resulting from common mistakes are often included in the five answer choices to trap you.
The AP Statistics free-response questions require not only that you perform the right computations but also that you communicate your reasoning and justify your answers clearly.
As the name suggests, the investigative task question invites you to investigate a situation and arrive at a solution. It might also require you to expand your knowledge of statistics a bit beyond the course curriculum.
Students are expected to bring a four function, scientific, or graphing calculator for them to use on both sections of the exam. AP scores are reported from 1 to 5.
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