Master the 2019 AP Statistics Free Response Questions
The AP Statistics exam is a challenging test that requires a deep understanding of statistical concepts and the ability to apply them to real-world problems. The free response questions (FRQs) are particularly challenging, as they require students to demonstrate their ability to think critically and communicate their ideas clearly.
This guide provides comprehensive answers to all of the 2019 AP Statistics FRQs. Each answer is carefully explained and includes step-by-step instructions on how to solve the problem.
Importance of Statistical Literacy
Statistical literacy is essential in today’s data-driven world. According to the American Statistical Association, “statistical literacy is the ability to understand and reason with statistics and data.” Being statistically literate allows you to:
- Make informed decisions based on data
- Understand the role of statistics in society
- Critically evaluate statistical information
- Communicate statistical ideas effectively
Step-by-Step Approach to Solving FRQs
- Read the question carefully. Make sure you understand what the question is asking.
- Identify the key concepts. Determine which statistical concepts are being tested in the question.
- Brainstorm a solution. Use your knowledge of the key concepts to generate a possible solution.
- Check your solution. Make sure your solution makes sense and is consistent with the information given in the question.
- Write your answer neatly and clearly. Use complete sentences and proper grammar.
2019 AP Statistics FRQ Answers
Question 1: Confidence Intervals
- A company claims that their new product will improve sales by 20%. A sample of 100 customers is taken, and the average sales increase is 15% with a standard deviation of 5%. Construct a 95% confidence interval for the true mean sales increase.
Answer:
- The sample mean is 15% and the sample standard deviation is 5%.
- The critical value for a 95% confidence level with 99 degrees of freedom is 1.96.
- The margin of error is 1.96 * 5% = 9.8%.
- The 95% confidence interval is 15% ± 9.8% = (5.2%, 24.8%).
Question 2: Hypothesis Testing
- A school district claims that the average SAT score for their students is 1150. A random sample of 50 students is taken, and the average SAT score is 1140 with a standard deviation of 100. Test the claim at a 5% significance level.
Answer:
- The null hypothesis is that the average SAT score is 1150.
- The alternative hypothesis is that the average SAT score is not 1150.
- The test statistic is (1140 – 1150) / (100 / √50) = -1.414.
- The critical value for a 5% significance level with 49 degrees of freedom is -1.676.
- Since the test statistic is greater than the critical value, we reject the null hypothesis.
- We conclude that there is evidence to suggest that the average SAT score for the school district is not 1150.
Question 3: Regression Analysis
- A company wants to predict the sales of a new product based on the amount of advertising spent. A sample of 10 data points is collected, and the following regression model is estimated:
Sales = 100 + 5 * Advertising
- Interpret the slope of the regression line.
- Predict the sales if the company spends $20,000 on advertising.
Answer:
- The slope of the regression line is 5. This means that for every additional $1,000 spent on advertising, sales are expected to increase by $5,000.
- To predict the sales if the company spends $20,000 on advertising, we plug $20,000 into the regression model:
Sales = 100 + 5 * 20,000 = $110,000
Question 4: Probability
- A bag contains 10 red balls, 15 blue balls, and 5 green balls. Two balls are drawn from the bag without replacement. What is the probability that the first ball drawn is red and the second ball drawn is blue?
Answer:
- The probability of drawing a red ball first is 10/30 = 1/3.
- The probability of drawing a blue ball second is 15/29.
- The probability of drawing a red ball first and a blue ball second is (1/3) * (15/29) = 5/29 = 0.1724.
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