AP Statistics t Intervals and t Tests for a Mean Test with Point Values (PDF)

AP Statistics math test: t Intervals and t Tests for a Mean – Maths PDF

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This inference one mean test for AP Statistics covers t intervals and t tests for a mean (Common Core AP STAT 7.1, AP STAT 7.2, AP STAT 7.3, AP STAT 7.4, AP STAT 7.5, HSS-IC.B.4), with a free PDF to print.

This 45-minute test covers the t distribution, one-sample t intervals and tests, and matched pairs. Follow State, Plan, Do, Conclude and write each conclusion in context.

Time and points

About this test

Grade: AP Statistics
Chapter: t Intervals and t Tests for a Mean
Standards: AP STAT 7.1, AP STAT 7.2, AP STAT 7.3, AP STAT 7.4, AP STAT 7.5, HSS-IC.B.4
Time: 45 minutes
Total: 20 points

Inference one mean test: questions

Question 1 – t interval [4 pts]

Weights of 10 packages (rounded to 0.5).

The weights (oz) of 10 randomly selected packages are 12.1, 13.4, 11.8, 12.9, 13.0, 12.5, 13.7, 12.2, 12.8, 13.1. (a) Check the conditions using the graph. (1 point) (b) Construct a 95% confidence interval for the mean weight. (2 points) (c) Interpret. (1 point)

Question 2 – t test [4 pts]

Two-sided p-value.

A random sample of 32 commuters has mean travel time 15.8 minutes with s = 3.2 minutes. Test whether the true mean differs from 15 minutes at alpha = 0.05. (State 1, Plan 1, Do 1, Conclude 1)

Question 3 – Matched pairs setup [2 pts]

Each of 20 students is timed on a puzzle with and without background music. Explain why a matched pairs procedure is appropriate and what the parameter is.

Question 4 – t* and z* [2 pts]

Normal and t.

Why is the critical value t* larger than z* for the same confidence level when n = 10? What happens as n increases?

Question 5 – Effect of changes [2 pts]

For a t interval, describe the effect on the margin of error of (a) increasing n, (b) raising the confidence level. (1 point each)

Question 6 – Conditions [2 pts]

Is a one-sample t procedure appropriate? (a) random sample of 12 with a dotplot that has one extreme outlier; (b) random sample of 45 with moderate right skew. (1 point each)

Question 7 – Interpret the p-value [2 pts]

A t test of H0: mu = 20 versus Ha: mu > 20 gives a p-value of 0.03. Interpret the p-value in context, where mu is the mean time (in minutes) to finish a quiz.

Question 8 – Degrees of freedom [2 pts]

A random sample of 18 students is used for a t interval. Give df and the 95% critical value t*.

Key facts behind this inference one mean test

Key facts

t distribution: bell-shaped, centered at 0, heavier tails; df = n – 1.
Interval: x-bar +/- t* s/sqrt(n); test: t = (x-bar – mu0)/(s/sqrt(n)).
Conditions: random, 10% condition, and Normal/Large Sample (population normal, n >= 30, or no strong skew or outliers).
As df grows, t* approaches z*.
Matched pairs: take differences and do a one-sample t procedure.

How to use this inference one mean 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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