Practice Statistical Significance in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A result is statistically significant when the p-value falls below a predetermined threshold (alpha, typically 0.05), indicating that the observed effect is unlikely to have occurred by random chance alone. Statistical significance is a binary decision criterion used in hypothesis testing — it does not measure the size or practical importance of the effect.

Statistical significance is a decision rule: before looking at data, you set a threshold (usually 5%). If your p-value is below this threshold, you declare the result 'significant' - meaning unlikely to be just random noise. It's not about importance; it's about confidence that something real is happening.

Example 1

hard
A drug trial finds a statistically significant reduction in blood pressure (p = 0.02). The mean reduction was 2 mmHg. Is this result practically significant?

Example 2

hard
Explain the difference between a Type I error and a Type II error in hypothesis testing.

Example 3

hard
A study with 10,000 participants finds a statistically significant difference in test scores between two teaching methods (p = 0.001), but the difference is only 0.5 points out of 100. Discuss.

Example 4

hard
A treatment improves average test scores by 12 points, but the p-value is 0.08. At \alpha = 0.05 is the result statistically significant, and could the effect still be practically important?
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