AP Stats Stats: Key Skills Assessed 3 — Questions and Answers
Question 1: A chi-square goodness-of-fit test is used to determine whether:
- Two quantitative variables are linearly related
- A sample mean differs from a known population mean
- Observed categorical frequencies match expected frequencies (Correct answer)
- Two population variances are equal
Correct answer: Observed categorical frequencies match expected frequencies
The chi-square goodness-of-fit test compares observed counts to expected counts for one categorical variable.
Question 2: In a simple linear regression model ŷ = a + bx, the slope b represents:
- The value of y when x equals zero
- The predicted change in y for a one-unit increase in x (Correct answer)
- The correlation coefficient between x and y
- The standard deviation of the residuals
Correct answer: The predicted change in y for a one-unit increase in x
The slope b is the predicted change in the response variable for each one-unit increase in the explanatory variable.
Question 3: If a distribution has a mean of 80 and a standard deviation of 10, what percentage of data falls between 60 and 100 according to the Empirical Rule?
- 68%
- 95% (Correct answer)
- 99.7%
- 50%
Correct answer: 95%
60 and 100 are each 2 standard deviations from the mean (80 ± 20), so approximately 95% of data falls in this range.
Question 4: A probability sample in which every member of the population has an equal chance of being selected is called a:
- Stratified random sample
- Cluster sample
- Simple random sample (Correct answer)
- Convenience sample
Correct answer: Simple random sample
A simple random sample (SRS) gives every individual an equal probability of selection.
Question 5: When the p-value of a hypothesis test is less than the significance level α, the correct conclusion is:
- Fail to reject the null hypothesis
- Accept the null hypothesis as true
- Reject the null hypothesis (Correct answer)
- Increase the sample size and retest
Correct answer: Reject the null hypothesis
A p-value below α means the data provides sufficient evidence to reject the null hypothesis.
Question 6: In an experiment, the placebo effect is best controlled by:
- Using a larger sample size
- Using a double-blind design (Correct answer)
- Randomly assigning treatments
- Using a stratified sample
Correct answer: Using a double-blind design
A double-blind design prevents both subjects and evaluators from knowing treatment assignments, controlling for placebo effects.
Question 7: Which statistic measures the strength and direction of the linear relationship between two quantitative variables?
- Standard deviation
- Coefficient of determination (r²)
- Correlation coefficient (r) (Correct answer)
- Interquartile range
Correct answer: Correlation coefficient (r)
The correlation coefficient r ranges from −1 to 1 and measures the strength and direction of a linear association.
AP Stats Stats: Key Skills Assessed 3
A chi-square goodness-of-fit test is used to determine whether: