AP Stats Stats: Key Skills Assessed 2 — Questions and Answers
Question 1: A researcher collects data on reaction times (ms) for 50 subjects. The distribution is strongly right-skewed. Which measure of center best describes the data?
- Mean
- Median (Correct answer)
- Mode
- Range
Correct answer: Median
The median is resistant to skewness and outliers, making it the better measure of center for skewed distributions.
Question 2: When constructing a 95% confidence interval for a population mean, which of the following changes would decrease the margin of error?
- Increasing the confidence level to 99%
- Decreasing the sample size
- Increasing the sample size (Correct answer)
- Increasing the population standard deviation
Correct answer: Increasing the sample size
A larger sample size reduces the standard error, which decreases the margin of error.
Question 3: A z-score of −2.1 for an observation means that the observation is:
- 2.1 standard deviations below the mean (Correct answer)
- 2.1 units below the mean
- 2.1% below the mean
- 2.1 standard deviations above the mean
Correct answer: 2.1 standard deviations below the mean
A z-score measures how many standard deviations an observation is from the mean; negative means below.
Question 4: In a two-sample t-test comparing group means, which condition is required for the test to be valid?
- Both populations must be exactly normal
- The samples must be collected from the same population
- The two samples must be independent of each other (Correct answer)
- Both sample sizes must be equal
Correct answer: The two samples must be independent of each other
Independence of the two samples is a required condition for a two-sample t-test.
Question 5: A scatterplot shows a curved, nonlinear relationship between x and y. Which action is most appropriate before performing linear regression?
- Remove outliers from the dataset
- Apply a transformation such as log(y) or √y (Correct answer)
- Increase the sample size
- Use a one-sample t-test instead
Correct answer: Apply a transformation such as log(y) or √y
Applying a transformation can linearize a curved relationship so that linear regression is appropriate.
Question 6: A Type I error in hypothesis testing occurs when:
- The null hypothesis is false and we fail to reject it
- The null hypothesis is true and we fail to reject it
- The null hypothesis is true and we reject it (Correct answer)
- The alternative hypothesis is true and we reject the null
Correct answer: The null hypothesis is true and we reject it
A Type I error is rejecting a true null hypothesis, also called a false positive.
Question 7: Which of the following best describes the power of a hypothesis test?
- The probability of making a Type I error
- The probability of rejecting the null hypothesis when it is false (Correct answer)
- The probability of failing to reject the null hypothesis when it is true
- The width of the confidence interval
Correct answer: The probability of rejecting the null hypothesis when it is false
Power is the probability of correctly rejecting a false null hypothesis; it equals 1 − β.
AP Stats Stats: Key Skills Assessed 2
A researcher collects data on reaction times (ms) for 50 subjects.
The distribution is strongly right-skewed.
Which measure of center best describes the data?