AP Statistics Practice Quiz: Confidence Intervals 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 z-interval for a proportion
B) A two-sample t-interval for a difference in means
C) A t-interval for the slope
D) A chi-square test for independence
Correct Answer: C
Content point 1 and 5 state that the appropriate confidence interval procedure for a slope of a regression model is a t-interval for the slope.
A) The standard error of the slope
B) The slope of the line of best fit, b
C) The critical value, t*
D) The y-intercept of the line of best fit
Correct Answer: B
Content point 9 specifies that the point estimate for the slope of a regression model is the slope of the line of best fit, b.
A) The distribution of the explanatory variable (x) must be approximately normal.
B) The sample size must be less than 10% of the population size.
C) The standard deviation of the response variable (y) does not vary with x.
D) The data must be collected from a randomized, controlled experiment.
Correct Answer: C
Content point 6 lists the required conditions, which include checking that the standard deviation of y does not vary with x.
A) b ± t*(SE of b)
B) t* ± b(SE of b)
C) SE of b ± t*(b)
D) b ± z*(SE of b)
Correct Answer: A
Content point 10 provides the formula for the interval estimate for the slope as b ± t*(SE of b).
A) By dividing the critical value t* by the standard error of the slope.
B) By multiplying the point estimate (b) by the critical value t*.
C) By multiplying the critical value t* by the standard error of the slope.
D) By adding the point estimate (b) to the standard error of the slope.
Correct Answer: C
Content point 7 states that the margin of error for the slope is t* times the standard error of the slope.
A) The relationship between the variables is linear.
B) The data points are independent.
C) The responses are approximately normal for each value of x.
D) The sample size is greater than or equal to 30.
Correct Answer: D
Content point 6 lists the required conditions: linear relationship, independent data, constant standard deviation of y, and approximately normal responses. A specific sample size condition like n ≥ 30 is not listed as a requirement for this procedure.
A) (3.7, 6.7)
B) (3.2, 7.2)
C) (2.2, 8.2)
D) (5.2, 7.2)
Correct Answer: C
First, calculate the margin of error: t* times the standard error of the slope = 2.0 * 1.5 = 3.0 (Content 7). Then, calculate the interval: b ± margin of error = 5.2 ± 3.0, which results in the interval (2.2, 8.2) (Content 10).
A) The mean of x and the mean of y
B) The correlation coefficient and the sample size
C) The standard deviation of the residuals and the standard deviation of the x-values
D) The slope of the line of best fit and the y-intercept
Correct Answer: C
Content point 8 explicitly states that the formula for the standard error for the slope involves the standard deviation of residuals and the standard deviation of the x-values.
A) The point estimate
B) The interval estimate
C) The standard error
D) The margin of error
Correct Answer: D
Content point 7 defines the margin of error for the slope as t* times the standard error of the slope. This matches the component in the interval formula from Content 10.
A) That the relationship between the variables is linear.
B) That the sampling distribution of the slope is approximately normal, validating the use of a t-interval.
C) That the data points are independent of one another.
D) That the standard deviation of the residuals is constant.
Correct Answer: B
The normality condition for the responses (residuals) is necessary to ensure that the sampling distribution of the statistic (the slope, b) follows a t-distribution, which justifies the use of a t-interval for the slope, as identified in Content 5.
A) 2.0
B) 4.0
C) 10.5
D) 12.5
Correct Answer: D
The point estimate, b, is the center of the confidence interval. The center of the interval (10.5, 14.5) is calculated as (10.5 + 14.5) / 2 = 25.0 / 2 = 12.5. This is based on the structure of the interval b ± margin of error from Content 10.
A) 2.0
B) 4.0
C) 12.5
D) 25.0
Correct Answer: A
The margin of error is half the width of the confidence interval. The width is 14.5 - 10.5 = 4.0. Therefore, the margin of error is 4.0 / 2 = 2.0. This is derived from the interval structure b ± margin of error (Content 10) and the definition of the margin of error (Content 7).
A) The point estimate is the width of the interval estimate.
B) The interval estimate is centered around the point estimate.
C) The point estimate is the upper bound of the interval estimate.
D) The interval estimate is calculated by squaring the point estimate.
Correct Answer: B
Content 9 identifies the point estimate as b. Content 10 shows the interval estimate is calculated as b ± t*(SE of b). This formula demonstrates that the interval is centered around the point estimate, b.
A) A curved pattern in the scatterplot of the original data.
B) A fan shape in the residual plot.
C) A lack of a clear pattern in the residual plot.
D) A normal probability plot of the residuals that is a straight line.
Correct Answer: C
The condition that the relationship is linear (Content 6) is checked by examining the original scatterplot for a linear form and, more formally, by checking the residual plot for the absence of any leftover pattern. A lack of pattern supports the linear condition.
A) The SE of b will increase.
B) The SE of b will decrease.
C) The SE of b will remain unchanged.
D) The SE of b will become negative.
Correct Answer: B
Content 8 states the standard error of the slope involves the standard deviation of x-values. In the actual formula, the standard deviation of x is in the denominator. Therefore, a larger standard deviation of x will lead to a smaller standard error for the slope.
A) The confidence interval will become wider.
B) The confidence interval will become narrower.
C) The width of the confidence interval will not change.
D) The confidence interval will shift to the right.
Correct Answer: B
A smaller standard error of the slope (SE of b) will result in a smaller margin of error, since the margin of error is t* times the SE of b (Content 7). A smaller margin of error will produce a narrower confidence interval, as the interval is calculated by adding and subtracting the margin of error from the point estimate (Content 10).