AP Statistics Inference for the Slope of a Regression Line Test with Point Values (PDF)

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

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This inference slope test 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.

This 45-minute test covers LINER conditions, reading regression output, intervals and tests for a slope, and selecting an inference procedure. Follow State, Plan, Do, Conclude and answer in context.

Time and points

About this test

Grade: AP Statistics
Chapter: Inference for the Slope of a Regression Line
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
Time: 45 minutes
Total: 20 points

Inference slope test: questions

Question 1 – Interval for the slope [4 pts]

Output for weight lifted.

A random sample of 10 athletes’ weight lifted (pounds, y) was regressed on weeks of training (x). Use the output to (a) state the equation and interpret the slope (1 point) and (b) construct a 95% confidence interval for the true slope (2 points), and (c) interpret it (1 point).

Question 2 – Test for the slope [4 pts]

Two-sided p-value.

With the same output, test H0: beta = 0 versus Ha: beta not equal to 0 at alpha = 0.05. (Hypotheses 1, conditions 1, t and p-value 1, conclusion 1)

Question 3 – Conditions [3 pts]

A residual plot.

(a) Which conditions can be checked with this residual plot? (2 points) (b) Does it suggest a problem? (1 point)

Question 4 – Interpret r squared [2 pts]

A regression of weight lifted on weeks of training has R-Sq = 95.0%. Interpret it in context.

Question 5 – Reading output [2 pts]

An output line reads: Hours 0.84 0.31 2.71 0.014. Identify the slope, its standard error, the t statistic, and the p-value, and state the conclusion at alpha = 0.05.

Question 6 – Interval and test [2 pts]

A 99% interval for the slope is (0.12, 0.88). Without further calculation, what is the conclusion of a two-sided test of H0: beta = 0 at alpha = 0.01?

Question 7 – Degrees of freedom [1 pt]

A regression uses 25 data points. Find the degrees of freedom for inference about the slope.

Question 8 – Select a procedure [2 pts]

Choosing a procedure.

Name the procedure: (a) test if the proportion of voters favoring a measure is more than 0.5; (b) estimate the effect of one more hour of study on the mean score.

Key facts behind this inference slope test

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

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All AP Statistics chapters: AP Statistics math.

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