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📘 Lesson 11 of 11 · Statistics

🔬 Hypothesis Testing

Hypothesis testing is a formal procedure for deciding whether there's enough evidence in sample data to support a claim about a population.

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01 Key Concepts

Null Hypothesis (H0)

The default assumption of 'no effect' or 'no difference' that we test against, such as 'this new drug has no effect'.

Alternative Hypothesis (H1)

The claim we're trying to find evidence for, such as 'this new drug does have an effect'.

P-value

The probability of observing results at least as extreme as what was found, assuming the null hypothesis is true. A small p-value suggests the null hypothesis is unlikely.

Significance Level (alpha)

A threshold (commonly 0.05) set in advance; if the p-value is less than alpha, the result is considered 'statistically significant' and we reject the null hypothesis.

Type I and Type II Errors

Type I error: rejecting a true null hypothesis (a false alarm). Type II error: failing to reject a false null hypothesis (a missed effect).

02 Key Formulas

03 Solved Examples

Example 1 A test gives a p-value of 0.02, with significance level alpha = 0.05. What is the conclusion?
  1. Compare the p-value to alpha: 0.02 < 0.05.
  2. Since the p-value is less than alpha, the result is statistically significant.
Answer: Reject the null hypothesis — there is significant evidence for the alternative hypothesis
Example 2 A test gives a p-value of 0.20, with significance level alpha = 0.05. What is the conclusion?
  1. Compare the p-value to alpha: 0.20 is greater than 0.05.
  2. Since the p-value is not less than alpha, there isn't enough evidence to reject the null.
Answer: Fail to reject the null hypothesis — not enough evidence for the alternative
Example 3 A jury wrongly convicts an innocent person. Relate this to Type I and Type II errors, where H0 = 'innocent'.
  1. H0 (innocent) is true, but it was rejected (convicted) anyway.
  2. Rejecting a true null hypothesis is a Type I error.
Answer: This is a Type I error (false positive)

04 Practice Questions

1If p-value = 0.01 and alpha = 0.05, do we reject H0?
Yes, since 0.01 < 0.05
2If p-value = 0.08 and alpha = 0.05, do we reject H0?
No, since 0.08 > 0.05
3What does the null hypothesis typically represent?
The default assumption of no effect or no difference
4What is a Type II error?
Failing to reject a false null hypothesis (missing a real effect)
5What is the most common significance level used in practice?
0.05

📄 Hypothesis Testing — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet