AP Statistics Inference for the Difference of Two Means Test with Point Values (PDF)

AP Statistics math test: Inference for the Difference of Two Means – Maths PDF

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This two means test for AP Statistics covers inference for the difference of two means (Common Core AP STAT 7.6, AP STAT 7.7, AP STAT 7.8, AP STAT 7.9, HSS-IC.B.5), with a free PDF to print.

This 45-minute test covers two-sample t intervals and tests, conditions, and the choice between independent and paired designs. Follow State, Plan, Do, Conclude and write each conclusion in context.

Time and points

About this test

Grade: AP Statistics
Chapter: Inference for the Difference of Two Means
Standards: AP STAT 7.6, AP STAT 7.7, AP STAT 7.8, AP STAT 7.9, HSS-IC.B.5
Time: 45 minutes
Total: 20 points

Two means test: questions

Question 1 – Two-sample interval [4 pts]

Hours studied per week.

Independent random samples of students report their weekly study hours (see the table). (a) State and check the conditions. (1 point) (b) Construct a 95% confidence interval for mu_online – mu_in-person. (2 points) (c) Interpret the interval. (1 point)

Question 2 – Two-sample test [4 pts]

Two-sided p-value.

Using the same data, test whether the mean study times differ at alpha = 0.05. (Hypotheses 1, statistic 1, p-value 1, conclusion 1)

Question 3 – Paired or two-sample [3 pts]

For each study, name the correct procedure and the parameter: (a) the cholesterol of 15 patients before and after a diet; (b) the mean commute times of 30 randomly selected drivers and 30 randomly selected cyclists. (Procedure 1 each, parameter 1 total)

Question 4 – Standard error [2 pts]

Group 1: n = 25, s = 6. Group 2: n = 36, s = 9. Find the standard error of x-bar1 – x-bar2.

Question 5 – Normal condition [2 pts]

Two small samples.

The boxplots are from two small independent random samples (n = 12 each). Is a two-sample t procedure appropriate? Explain.

Question 6 – Interpret p-value [2 pts]

A two-sample t test of H0: mu1 = mu2 gives p = 0.003. Interpret the p-value and state the conclusion at alpha = 0.01.

Question 7 – Name the parameter [1 pt]

In the study of online and in-person students, define mu_1 – mu_2 in context.

Question 8 – Effect of changes [2 pts]

How does each change affect the width of a two-sample interval: (a) larger samples, (b) 99% instead of 95% confidence?

Key facts behind this two means test

Key facts

Parameter: mu1 – mu2; statistic: x-bar1 – x-bar2.
SE = sqrt(s1^2/n1 + s2^2/n2); df from the calculator, or min(n1 – 1, n2 – 1) conservatively.
Interval: (x-bar1 – x-bar2) +/- t* SE; test: t = (x-bar1 – x-bar2)/SE with H0: mu1 – mu2 = 0.
Conditions: independent random samples or random assignment; 10%; each group normal or n >= 30.
Same subjects measured twice or matched pairs: use a one-sample t on the differences.

How to use this two means 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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