2019 International Practice Exam Frq Ap Stats

2019 AP Statistics International Practice Exam FRQs: A Comprehensive Guide

The 2019 AP Statistics International exam presented students with a challenging set of free-response questions (FRQs). This guide provides a detailed breakdown of each question, offering insights into the concepts tested, common mistakes, and strategies for approaching similar problems on future exams. Mastering these FRQs will not only improve your understanding of AP Statistics but also enhance your problem-solving skills and exam preparedness.

Question 1: Exploring Relationships Between Variables

This question typically focuses on exploring relationships between two or more variables using methods like scatterplots, correlation, regression, and residual analysis. Expect questions that involve:

1.1 Interpreting Scatterplots and Correlation

Expect questions asking you to describe the direction, form, and strength of the relationship shown in a scatterplot. Remember to quantify the strength using the correlation coefficient (r), and interpret its value within the context of the problem. Don't just say "strong positive correlation"; explain what "strong" and "positive" mean in the specific context of the variables.

Example: If the scatterplot shows the relationship between hours studied and exam scores, a strong positive correlation indicates that as hours studied increase, exam scores tend to increase significantly.

1.2 Understanding and Interpreting Regression Models

Be prepared to interpret the slope and y-intercept of a least-squares regression line in context. Focus on understanding the meaning of the slope and intercept, not just their numerical values. For example, a slope of 2 in a model predicting exam scores based on hours studied means that for every additional hour studied, the predicted exam score increases by 2 points. Also, be ready to use the regression equation to make predictions and interpret the meaning of those predictions.

1.3 Analyzing Residuals

Analyzing residuals is crucial. Questions might ask you to create a residual plot and interpret its patterns. A random scatter of residuals suggests a good fit for the linear model; non-random patterns indicate potential problems with the linear model. Be able to explain what these patterns suggest about the appropriateness of the linear model and the presence of outliers or influential points.

Key Strategies for Question 1:

• Clearly label all graphs and diagrams. This is crucial for earning points.
• Use precise statistical language. Avoid vague terms like "strong" or "weak." Quantify your descriptions using numerical measures (e.g., r = 0.8 indicates a strong positive correlation).
• Show your work. Write out the calculations and explain your reasoning clearly.
• Context is key. Always relate your statistical findings back to the context of the problem.

Question 2: Inference for Means

This section often delves into hypothesis testing and confidence intervals for population means. Be prepared for questions involving:

2.1 One-Sample t-test

A common scenario involves testing a hypothesis about a single population mean using a one-sample t-test. Ensure you understand the conditions for using a t-test (random sample, approximately normal distribution, independent observations). You'll need to state hypotheses, calculate the test statistic, find the p-value, and draw conclusions in context. Remember to specify whether you are performing a one-tailed or two-tailed test.

2.2 Two-Sample t-test

This involves comparing the means of two independent populations. Pay close attention to whether the variances are assumed to be equal or unequal. The procedure for calculating the test statistic differs depending on this assumption. Again, clearly state your hypotheses, calculate the test statistic, and interpret your results within the given context.

2.3 Confidence Intervals for Means

You'll need to be able to construct and interpret confidence intervals for a single population mean or the difference between two population means. Understand the meaning of the confidence level and the margin of error. Be able to explain what a confidence interval tells us about the likely range of the population parameter.

Key Strategies for Question 2:

• Clearly state your hypotheses. Define the parameters involved (e.g., μ₁, μ₂).
• Check conditions for inference. Verify that the necessary conditions are met before performing the test.
• Show your work. Document your calculations clearly, including the formula used and the values substituted.
• Write a conclusion in context. Relate your findings back to the original question and the problem's context. Avoid simply stating "reject the null hypothesis" – explain what that means in terms of the specific problem.

Question 3: Inference for Proportions

This section often involves hypothesis testing and confidence intervals for population proportions. Prepare for questions involving:

3.1 One-Sample z-test for Proportions

This involves testing a hypothesis about a single population proportion. Remember the conditions for using a z-test for proportions (random sample, large sample size, independence). You will need to calculate the test statistic, find the p-value, and draw a conclusion, all within the context of the problem.

3.2 Two-Sample z-test for Proportions

This compares the proportions of two independent populations. Similar to the two-sample t-test, you'll need to state hypotheses, calculate the test statistic, and draw conclusions, all properly contextualized.

3.3 Confidence Intervals for Proportions

Expect questions involving the construction and interpretation of confidence intervals for a single population proportion or the difference between two population proportions. Understand the relationship between the confidence level, margin of error, and sample size.

Key Strategies for Question 3:

• Use appropriate notation. Clearly define the parameters (e.g., p₁, p₂) and the sample proportions (e.g., p̂₁, p̂₂).
• Check conditions. Before performing any tests, verify that the sample size is large enough and that the data meets the independence criterion.
• Interpret results in context. Explain your findings in relation to the specific problem you are addressing.

Question 4: Chi-Square Tests

This section frequently involves chi-square tests for independence or goodness-of-fit. Be prepared for questions involving:

4.1 Chi-Square Test for Goodness-of-Fit

This tests whether observed data fit a hypothesized distribution. You'll need to calculate expected counts, the chi-square test statistic, the degrees of freedom, and the p-value. Remember to check the conditions for using a chi-square test (random sample, expected counts sufficiently large).

4.2 Chi-Square Test for Independence

This tests whether two categorical variables are independent. You'll construct a contingency table, calculate expected counts, the chi-square test statistic, the degrees of freedom, and the p-value. Again, make sure to check the necessary conditions before performing the test.

Key Strategies for Question 4:

• Construct a clear contingency table. Organize your data effectively for easy calculation of expected counts.
• Show your calculations. Detail how you arrived at your chi-square statistic and degrees of freedom.
• State your conclusion in the context of the problem. Explain what the results suggest about the independence of the variables or the goodness of fit to the hypothesized distribution.

General Strategies for All FRQs:

• Read the question carefully. Understand exactly what the question is asking before you begin.
• Clearly define any variables or parameters. Use proper notation consistently.
• Show all your work. Even if your final answer is incorrect, you may receive partial credit for showing your steps.
• Use proper statistical terminology. Avoid vague language and use precise terminology throughout your response.
• Explain your reasoning. Don't just provide answers; justify your choices and conclusions.
• Contextualize your findings. Relate your statistical results back to the problem's context.
• Check your work. Review your calculations and explanations before submitting your answers.

By thoroughly understanding these concepts and practicing with past exams, you will significantly improve your ability to answer AP Statistics FRQs effectively and confidently. Remember that consistent practice and a solid grasp of the underlying statistical principles are key to success on the exam. Good luck!