The College Board released the AP Statistics 2022 Free Response Questions (FRQs) on Monday, May 1, 2023. The questions cover a wide range of topics, including:
- Exploring Data
- Sampling and Experimentation
- Probability
- Statistical Inference
Exploring Data
The Exploring Data FRQ asked students to analyze a data set on the heights of students in a certain school. Students were asked to create a histogram, describe the distribution of the data, and identify any outliers.
Answer:
The histogram of the data is shown below. The distribution is roughly normal, with a mean of 68 inches and a standard deviation of 4 inches. There are two outliers, one at 50 inches and one at 80 inches.
[Image of a histogram of the heights of students in a certain school]
Sampling and Experimentation
The Sampling and Experimentation FRQ asked students to design a study to estimate the proportion of students at their school who own a car. Students were asked to describe their sampling method, sample size, and method of data collection.
Answer:
We could use a simple random sample of students from the school to estimate the proportion of students who own a car. We could select a sample of 100 students from the school directory using a random number generator. We could then survey these students to determine whether or not they own a car.
Probability
The Probability FRQ asked students to calculate the probability of drawing two aces from a deck of cards. Students were asked to use the rules of probability to show their work.
Answer:
The probability of drawing two aces from a deck of cards is:
P(two aces) = P(first ace) * P(second ace) = (4/52) * (3/51) = 1/221
Statistical Inference
The Statistical Inference FRQ asked students to test the hypothesis that the mean weight of a certain type of apple is equal to 10 ounces. Students were asked to conduct a hypothesis test and interpret the results.
Answer:
We can conduct a two-sample t-test to test the hypothesis that the mean weight of a certain type of apple is equal to 10 ounces. The null hypothesis is:
H0: mu = 10
The alternative hypothesis is:
Ha: mu != 10
We will use a significance level of 0.05.
The sample mean weight of a certain type of apple is 10.5 ounces. The sample standard deviation is 1.5 ounces. The sample size is 30.
The test statistic is:
t = (10.5 - 10) / (1.5 / sqrt(30)) = 2.12
The p-value is:
p-value = 2 * P(t < -2.12) = 0.042
Since the p-value is less than the significance level, we reject the null hypothesis. We conclude that there is evidence to suggest that the mean weight of a certain type of apple is not equal to 10 ounces.
Conclusion
The AP Statistics 2022 FRQs cover a wide range of topics, and students need to be well-prepared in order to do well on the exam. By studying the material and practicing with sample questions, students can improve their chances of success.