Percentages in Everyday Problems
Parts, wholes, change, and claims
Math workbook
Intro Statistics: Sampling and Inference: Study design, sampling variation, intervals and tests
Intro CollegeLevel 5
About this book
Know what your data can support, and say exactly that.
This workbook is a companion for an introductory college statistics course. It starts with study design: who a sample can describe, and when a study can support a claim about cause. Simulations then show how a statistic varies from sample to sample and what a standard error measures. Learners build and word confidence intervals, check method conditions, and read p-values without turning them into probabilities about hypotheses. Every module follows the same pattern: explain, worked example, guided and independent practice, review and a checkpoint. The answer key at the back gives each answer, its reasoning, a common error and a reteaching cue.
- Separate random sampling from random assignment
- See sampling variation through simulation
- Build and word confidence intervals with conditions
- Read p-values carefully and weigh effect size
- Explanatory key with common errors and reteach cues
For intro college learners who can already describe distributions, find means and use basic probability.
Look inside
What this book covers
Covered
In scope: random sampling and random assignment; simulated sampling distributions; standard error; 95% intervals for one proportion and one mean; tests by simulation and a one-sample z test; sample SD, z-scores and normal tables; p-values, Type I and II errors, and effect size.
Not covered
Not in scope: two-sample t formulas, chi-square tests, regression inference and Bayesian methods.
Before you start
Before you start, you need to describe distributions, find means, proportions and percents, use the 68–95–99.7 rule and find simple probabilities.
Things to have
Calculators are allowed.
Notice
Pictures in this book are simplified learning models. Check answers with the explanations at the back of the book.
The steps in this book
- Step 1: Readiness Check
Check the skills you need before you begin. If something feels tricky, an adult can help you start in the right place.
- Step 2: Concept
Read a short, clear explanation of the new idea and the words that go with it.
- Step 3: Worked Example
Watch the idea being used, one step at a time, in a worked example.
- Step 4: Guided Practice
Practice with prompts and help cues. The help gets smaller as you get stronger.
- Step 5: Independent Practice
Practice on your own with different kinds of questions, and explain your thinking.
- Step 6: Review
Look back at earlier learning so it stays strong, then check where to go next.
- Step 7: Answers and Explanations
Check your answers. Each answer explains why, names a common mistake, and shows how to fix it.
What is in the book
The modules
- Module 1: Study design sets the limitsPages 5–14
- Module 2: Sampling distributions explain uncertaintyPages 15–24
- Module 3: Intervals express a method’s uncertaintyPages 25–34
- Module 4: Tests assess compatibility with a modelPages 35–44
Contents
- Readiness check, pp. 3–4. Before Module 1. Its table tells you where to start.
- Modules, pp. 5–44
- Checkpoints, pp. 14, 24, 34, 44. The last page of each module.
- Mixed review, pp. 45–48. Questions from across the book, mixed together.
- Exit check, pp. 49–50. A last check across the book.
- Reflect and repair, p. 51
- Try again, p. 52. Fresh questions like those in the exit check.
- Further practice, pp. 53–56. More pages of step 5, Independent Practice.
- Extra practice, pp. 57–58
- Answers and explanations, pp. 59–70. Notes in this part are headed “Why”, “Common mistake”, “Help” and “Look for”.
Other books it mentions
Before this book
Statistics: Describe and Compare Data
Displays, center, spread, and fair comparisons
Probability: Model Chance and Evaluate Risk
Chance models, conditional data and risk