AP Statistics Practice Quiz: Setting Up a Test for the Slope of a Regression Model
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 16 questions to check your progress.
Question 1 of 16
All Questions (16)
A) A t-test for a slope
B) A chi-square test for independence
C) A two-sample z-test for means
D) A one-sample t-test for a mean
Correct Answer: A
The provided content explicitly states that 'The appropriate test for the slope of a regression model is a t-test for a slope.'
A) A test for the y-intercept of the regression model
B) A t-test for the slope of the regression model
C) A chi-square test of association
D) A two-sample t-test for the difference in mean scores
Correct Answer: B
To determine if a significant linear relationship exists, one must test the slope of the regression model. The content identifies the appropriate method for this as a t-test for a slope.
A) H0: β = β₀
B) H0: b = b₀
C) H0: μ₁ = μ₂
D) H0: p = p₀
Correct Answer: A
The content states, 'The null hypothesis for a t-test for a slope is H0: beta = beta0'. The Greek letter beta (β) represents the population slope, while β₀ is the hypothesized value.
A) H0: β = 1
B) H0: β > 0
C) H0: β = 0
D) H0: β ≠ 0
Correct Answer: C
To test for the existence of any linear relationship, the null hypothesis posits that the population slope (β) is zero, which indicates no linear relationship. The general form is H0: β = β₀, and in this common case, the hypothesized value β₀ is 0.
A) Ha: β = 0
B) Ha: β < 0
C) Ha: β ≠ 0
D) Ha: β > 0
Correct Answer: D
The researcher expects a positive relationship (as one variable increases, the other increases). This translates to a population slope (β) that is greater than zero. Therefore, the appropriate one-sided alternative hypothesis is Ha: β > 0.
A) Ha: β ≠ 0
B) Ha: β > 0
C) Ha: β = 0
D) Ha: β < 0
Correct Answer: A
A two-sided alternative hypothesis is used when the researcher is interested in detecting a relationship in either a positive or negative direction. This is represented by Ha: β ≠ 0.
A) H0: β = 0 vs. Ha: β > 0
B) H0: β = 0 vs. Ha: β ≠ 0
C) H0: β = 0 vs. Ha: β < 0
D) H0: β < 0 vs. Ha: β = 0
Correct Answer: C
The null hypothesis should assume no linear relationship (β = 0). The economist's claim is for a negative relationship, which means the population slope would be less than zero. Therefore, the appropriate alternative hypothesis is Ha: β < 0.
A) The sample size must be greater than 30.
B) The data must come from a randomized experiment.
C) The standard deviation of the response variable y is constant for all values of the explanatory variable x.
D) The explanatory variable x must be normally distributed.
Correct Answer: C
Based on the provided content, one of the four required conditions to check is that the 'standard deviation of y is constant'. The other options are not required conditions for this specific test.
A) The relationship between the variables is linear.
B) The observations are independent.
C) The sample of the explanatory variable x is selected randomly from a normal population.
D) For each value of x, the corresponding responses of y are normally distributed.
Correct Answer: C
The required conditions are that the relationship is linear, data are independent, the standard deviation of y is constant, and responses are normal for each x. There is no requirement that the explanatory variable x be normally distributed.
A) To ensure that the standard deviation of y is the same for all x-values.
B) To ensure that a straight line is an appropriate model for the relationship between the variables.
C) To ensure that individual data points do not influence each other.
D) To ensure that the response variable follows a t-distribution.
Correct Answer: B
The 'Linear' condition requires checking that the underlying relationship between the explanatory variable (x) and the response variable (y) is, in fact, linear, making a straight line an appropriate model.
A) The explanatory and response variables are not correlated.
B) The individual observations are independent of one another.
C) The residuals are normally distributed.
D) The slope and the y-intercept of the regression line are independent.
Correct Answer: B
The independence condition refers to the individual observations in the dataset. It means that knowing the outcome of one observation should not provide information about the outcome of another.
A) The distribution of the explanatory variable (x) must be approximately normal.
B) The overall distribution of the response variable (y) must be approximately normal.
C) For any given value of x, the corresponding y-values are normally distributed.
D) The sample size must be large enough for the Central Limit Theorem to apply.
Correct Answer: C
The 'Normal' condition specifically requires that 'responses are normal for each x.' This means that for any fixed value of the explanatory variable, the distribution of the possible responses for y follows a normal distribution.
A) The variability of the explanatory variable x is the same across its range.
B) The variability of the response variable y is the same for all values of x.
C) The sample standard deviation of y is equal to the population standard deviation of y.
D) The data points all lie exactly on the regression line.
Correct Answer: B
This condition means that the spread (measured by standard deviation) of the y-values around the true regression line is the same regardless of the x-value. The content states this as 'standard deviation of y is constant'.
A) The sample size is large and the x-values are normally distributed.
B) The standard deviation of y is constant for each x, and the responses of y are normal for each x.
C) The data was collected from a simple random sample and the population is at least 10 times the sample size.
D) The correlation coefficient is strong and the residuals sum to zero.
Correct Answer: B
The four conditions are: Linear, Independent, Normal, and Equal Standard Deviation. The student has checked the first two, so they must still check that the 'standard deviation of y is constant' and that 'responses are normal for each x'.
A) Hypothesis: H0: b = 0; Condition: The distribution of x-values is normal.
B) Hypothesis: H0: β = 0; Condition: The relationship between the variables is linear.
C) Hypothesis: H0: β ≠ 0; Condition: The observations are dependent.
D) Hypothesis: H0: b = β; Condition: The standard deviation of x is constant.
Correct Answer: B
A valid null hypothesis tests the population slope (β), commonly H0: β = 0. A required condition is that the relationship between the variables is linear. Option B correctly lists both. Option A uses the sample slope (b). Option C has an invalid null hypothesis form and an incorrect condition. Option D has an invalid hypothesis and an incorrect condition.
A) Check if the ages of the cars are normally distributed.
B) Check if the overall distribution of selling prices is normally distributed.
C) Check if the selling prices for cars of a specific age (e.g., 5-year-old cars) are normally distributed.
D) Check if the sample of cars was selected using an independent random sampling method.
Correct Answer: C
The 'Normal' condition states that 'responses are normal for each x'. In this context, x is the age and y is the selling price. Therefore, the condition requires checking if the selling prices (y) for a specific age (x) are normally distributed. It does not require the overall distribution of x or y to be normal.