Practice P-Value in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The probability of observing a test statistic at least as extreme as the one computed from the sample data, assuming the null hypothesis H_0 is true.
The p-value answers: 'If nothing special is going on (H_0 is true), how surprising is my data?' A tiny p-value means the data would be very rare under H_0, so maybe H_0 is wrong. Think of it like this: you flip a coin 100 times and get 92 heads. If the coin is fair, the chance of that happening is astronomically small (tiny p-value)—so you'd conclude the coin is probably not fair.
Example 1
mediumA hypothesis test produces z=2.3 for a two-tailed test. Calculate the p-value and interpret it at both \alpha=0.05 and \alpha=0.01.
Example 2
hardCorrect the following misconceptions about p-values: (a) 'p=0.03 means there's a 3% chance H₀ is true.' (b) 'p=0.03 means the effect is large.'
Example 3
easyA one-tailed test has z=1.7. Find the p-value and determine if we reject H_0 at \alpha=0.05.
Example 4
hardStudy A: n=50, p=0.04, effect size d=0.15 (tiny). Study B: n=10, p=0.06, effect size d=0.8 (large). Discuss which study's result is more practically meaningful and why we shouldn't rely solely on p-values.