Track 8 · Hypothesis Testing · Lesson 4 of 14
Significance level and errors
Use a significance level to make a decision, and explain the two kinds of error a test can make and how α, β and power trade off.
A food-safety lab tests batches for contamination. Declaring a clean batch contaminated wastes a day's production; missing a contaminated batch can make people ill. Every testing decision risks one of these two errors, and choosing α is choosing which risk you are more willing to take.
A p-value measures evidence; a decision needs a threshold. The significance level α is the threshold fixed before the data are seen: reject H0 when , otherwise do not reject. Common choices are 0.05 and 0.01, but α should reflect the cost of a false alarm in context — there is nothing magical about 0.05.
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Make a decision by comparing the p-value with a significance level fixed in advance
- Distinguish Type I errors (false positives) from Type II errors (false negatives)
- Compute a rejection region and the power of a z-test for a specific alternative
- Explain the trade-off between α and β, and choose α from the costs of each error