AP Statistics t Intervals and t Tests for a Mean Test with Point Values (PDF)
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.
Time and points
- 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]
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]
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]
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
- 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.
Free printable PDF
AP Statistics t Intervals and t Tests for a Mean Test with Point Values
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