AP Statistics Inference for the Slope of a Regression Line Test Solutions and Scoring (PDF)

AP Statistics math test solutions: Inference for the Slope of a Regression Line – Maths PDF

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This inference slope test answers for AP Statistics covers inference for the slope of a regression line (Common Core AP STAT 9.1, AP STAT 9.2, AP STAT 9.3, AP STAT 9.4, AP STAT 9.5, AP STAT 9.6, HSS-ID.B.6), with a free PDF to print.

Each solution is followed by a scoring guide. Award points for correct conditions, the right df, the correct interval or test statistic, and a conclusion that mentions the true slope in context.

AP Statistics · Common Core State Standards: AP STAT 9.1, AP STAT 9.2, AP STAT 9.3, AP STAT 9.4, AP STAT 9.5, AP STAT 9.6, HSS-ID.B.6

Inference slope test answers: worked solutions

Question 1 – Interval for the slope [4 pts]

Interval for beta.

(a) \(\hat{y}=9.800+2.036x\); each extra week adds about 2.04 pounds to the predicted weight. (b) \(df=8,\ t^{*}=2.306,\ ME=0.380\), interval (1.657, 2.416). (c) We are 95% confident the true slope is in that interval: each extra week of training raises the mean weight lifted by that many pounds.

(1.657, 2.416) pounds per week.

Scoring: 1 point for equation and slope interpretation, 1 point for t* and ME, 1 point for the interval, 1 point for the interpretation in context.

Question 2 – Test for the slope [4 pts]

Two-sided p-value.

\(H_0:\beta=0,\ H_a:\beta\neq 0\). Conditions (LINER) are assumed checked: linear pattern, independent random sample, roughly normal residuals, equal spread. \(t=12.37,\ df=8\), p-value \(=0.0000\).

Reject H0: convincing evidence of a linear relationship between weeks of training and weight lifted.

Scoring: 1 point for hypotheses with the parameter, 1 point for the conditions, 1 point for t and the p-value, 1 point for the conclusion in context.

Question 3 – Conditions [3 pts]

A residual plot.

(a) Linear (no curve) and Equal variance (constant spread). (b) No problem is visible; the spread is about the same everywhere.

Linear and Equal variance; no problem.

Scoring: 1 point for each condition, 1 point for the conclusion.

Question 4 – Interpret r squared [2 pts]

R-squared is the proportion of variation explained by the linear model.

About 95% of the variation in weight lifted is explained by its linear relationship with weeks of training.

Scoring: 1 point for the percent, 1 point for context.

Question 5 – Reading output [2 pts]

Slope 0.84, SE 0.31, t = 2.71, P = 0.014.

0.014 < 0.05: reject H0; there is convincing evidence of a linear relationship.

Scoring: 1 point for identifying the four values, 1 point for the conclusion.

Question 6 – Interval and test [2 pts]

0 is outside the interval.

Reject H0: convincing evidence that beta is not 0.

Scoring: 1 point for noting 0 is outside, 1 point for the conclusion.

Question 7 – Degrees of freedom [1 pt]

\(n-2=23\).

23.

Scoring: 1 point for 23.

Question 8 – Select a procedure [2 pts]

Choosing a procedure.

(a) One-proportion z test. (b) t interval for the slope.

(a) one-proportion z test; (b) t interval for the slope of the regression line.

Scoring: 1 point each.

Total score

Total

20 points

Key facts behind this inference slope test answers

Key facts

Parameter: true slope beta; statistic: sample slope b; df = n – 2.
Interval: b +/- t* SE_b; test: t = (b – 0)/SE_b for H0: beta = 0.
LINER: Linear, Independent, Normal residuals, Equal variance, Random.
Computer output gives b, SE_b, t, and the two-sided P in the row for the explanatory variable.
If the interval contains 0, there is no convincing evidence of a linear relationship.

How to use this inference slope test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

Download the inference slope test answers as a PDF with the button below and keep it with your notes.

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