AP Statistics FRQ Practice

1. Descriptive Statistics and Data Analysis

Question:

A group of students were surveyed about the number of hours they spend on homework each week. The data collected is as follows:

Data: 3, 4, 5, 5, 6, 7, 8, 8, 9, 10, 12

(a) Find the mean, median, and mode of the data.

(b) Calculate the standard deviation of the data.

Response Guidelines:

Part (a):
To find the mean, sum all the data points and divide by the number of data points.
To find the median, arrange the data in ascending order and find the middle value. If there is an even number of data points, take the average of the two middle values.
To find the mode, identify the value that occurs most frequently in the data set.
Part (b):
The standard deviation measures the spread of the data points. Calculate the variance first by finding the squared differences from the mean, then take the square root of the variance.
Part (c):
Explain how the mean, median, mode, and standard deviation describe the central tendency and spread of the data.

2. Probability and Random Variables

Question:

A bag contains 3 red balls and 5 green balls. If two balls are drawn randomly without replacement, what is the probability that both balls are red?

Response Guidelines:

Use the formula for probability of dependent events. The probability of drawing a red ball on the first draw is 3/8, and the probability of drawing another red ball, given that one red ball has already been drawn, is 2/7.

3. Hypothesis Testing

Question:

A researcher wants to test if the mean height of a population of students is 65 inches. A random sample of 30 students is taken, and the sample mean height is 66 inches with a standard deviation of 4 inches. Perform a hypothesis test at the 0.05 significance level to determine if the population mean is different from 65 inches.

(a) State the null and alternative hypotheses.

(b) Calculate the test statistic.

Response Guidelines:

Part (a):
The null hypothesis (H0) states that the population mean height is 65 inches, while the alternative hypothesis (Ha) states that the population mean height is not 65 inches (two-tailed test).
Part (b):
Use the t-test formula to calculate the test statistic: t = (x̄ - μ) / (s / √n),
where x̄ = sample mean, μ = population mean, s = sample standard deviation, and n = sample size.
Part (c):
Use the test statistic to find the p-value. Compare the p-value to the significance level (0.05) to make a decision about the null hypothesis.

Grading Rubric for AP Statistics FRQs

1. Descriptive Statistics and Data Analysis

Part (a):
- 0-1 points: Incorrect or incomplete calculation of the mean, median, or mode.
- 2 points: Correctly calculates the mean, median, and mode.
Part (b):
- 0-1 points: Incorrect or incomplete calculation of the standard deviation.
- 2 points: Correctly calculates the standard deviation.
Part (c):
- 0-1 points: Incorrect or incomplete interpretation of the measures of central tendency and dispersion.
- 2 points: Correctly interprets the measures of central tendency and dispersion.

2. Probability and Random Variables

Part (a):
- 0-1 points: Incorrect or incomplete calculation of probability.
- 2 points: Correctly calculates the probability of both balls being red.

3. Hypothesis Testing

Part (a):
- 0-1 points: Incorrect null and alternative hypotheses.
- 2 points: Correctly states the null and alternative hypotheses.
Part (b):
- 0-1 points: Incorrect or incomplete calculation of the test statistic.
- 2 points: Correctly calculates the test statistic.
Part (c):
- 0-1 points: Incorrect or incomplete calculation of the p-value and decision about the null hypothesis.
- 2 points: Correctly calculates the p-value and makes a correct decision about the null hypothesis.

Sample Grading Breakdown (for one FRQ)

Descriptive Statistics and Data Analysis: 6 points
Probability and Random Variables: 2 points
Hypothesis Testing: 6 points
Total: 14 points (for all three FRQs combined)