QM210
Critical Value Estimator
Given a hypothesis test setup, can you identify the correct critical value? Test your knowledge of Z and T tables across real business scenarios.
How It Works
- You will face 10 hypothesis test scenarios with business context
- Each round shows the test type (Z or T), significance level, tail direction, and degrees of freedom
- Select the correct critical value from 4 multiple-choice options
- After answering, see where the critical value falls on the distribution curve
- Earn 10 points per correct answer (100 max)
- Grade scale: A (90+), B (80+), C (70+), D (60+), F (below 60)
Game Over!
You scored out of 100
Your Results
| # | Test Setup | Correct Value | Result |
|---|
Tips for Reading T and Z Tables
Critical values are the gatekeepers of hypothesis testing. Here is how to find them efficiently:
- Z-table: For common alphas, memorize the key values: 1.645 (one-tailed 0.05), 1.96 (two-tailed 0.05), 2.326 (one-tailed 0.01), 2.576 (two-tailed 0.01)
- T-table: Look up the row for your degrees of freedom (df = n - 1) and the column for your alpha and tail direction
- Two-tailed tests split alpha between both tails, so use alpha/2 when looking up the value in a one-tail table
- As df increases, T critical values approach Z critical values — the T distribution converges to the standard normal
- Lower alpha means a higher critical value — you need stronger evidence to reject H0